Searches for Massive Highly Ionising Particles at the ATLAS Experiment and in Polar Volcanic Rocks, and Performance Studies of the First Level ATLAS Trigger System

Home , Micro black hole, Stable massive particles, TOTEM experiment

Katarina Bendtz

Doctoral Thesis in Physics

Department of Physics Stockholm University Stockholm 2016 ii

Doctoral Thesis in Physics

Searches for Massive Highly Ionising Particles at the ATLAS Experiment and in Polar Volcanic Rocks, and Performance Studies of the First Level ATLAS Trigger System

Katarina Bendtz

Department of Physics Stockholm University Roslagstullsbacken 21

Stockholm, Sweden 2016 ISBN 978-91-7649-293-2 c Katarina Bendtz, 2016

Printed by Holmbergs, Malm¨o,Sweden, 2016.

Cover illustration by Julia Eriksson Abstract

The Standard Model (SM) of particle physics describes the elementary particles and their interactions. Despite passing a number of high precision falsification tests, it is nevertheless argued that the SM suffers from a number of shortcomings. Many Beyond the Standard Model (BSM) theories have therefore been postulated. Exotic highly ionising particles such as magnetic monopoles and Highly Electrically Charged Objects (HECOs), with masses at or above the TeV-scale, are predicted in many of these theories. Monopoles arise naturally in grand unification theories. Proposed candidates for HECOs are Q-balls, strangelets and micro-black hole remnants. The Large Hadron Collider (LHC) at CERN is the world’s largest and most powerful particle accelerator, colliding protons at centre-of-mass energies up to 13 TeV. One of the main purposes of the LHC is to search for particles beyond the SM. The research presented in this thesis comprises a search for magnetic monopoles and HECOs at one of the largest of the LHC detectors, the ATLAS detector. In addition, studies were made on the performance of the ATLAS trigger system, which is responsible for making the initial online selection of interesting proton-proton events. The search for monopoles and HECOs at ATLAS was conducted using a customized trigger and selection variables optimized for the non- standard particle signature in ATLAS. The dataset corresponds to an integrated luminosity of 7.0 fb−1 and the centre-of-mass energy was 8 TeV. No events were observed and upper limits on production cross-sections were set for monopoles and HECOs of masses 200-2500 GeV and charges in the range 0.5 2.0 gD, where gD is the Dirac charge, and 10 60 e, − − respectively. Magnetic monopoles were also sought in polar volcanic rock using a SQUID magnetometer at ETH, Zürich. No candidates were found leading to limits on the monopole density in polar igneous rocks of 9.8 10−5/gram. ·

iii iv This thesis is dedicated to everyone.

v vi Publications Included in the Thesis

The following papers, referred to in the text by their Roman numerals, are included in this thesis.

Paper I ATLAS Collaboration. The ATLAS transverse-momentum trigger performance at the LHC in 2011, ATLAS-CONF-2014-002 CERN February 11, 2014.

Paper II ATLAS Collaboration. Search for magnetic monopoles and stable particles with high electric charges in 8 TeV pp collisions with the ATLAS detector, Phys. Rev. D, 93, 052009 (2016).

Paper III K. Bendtz, D. Milstead, H.-P. H¨achler, A. M. Hirt, P. Mer- mod, P. Michael, T. Sloan, C. Tegner and S. B. Thorarinsson. Search for magnetic monopoles in polar volcanic rocks, Phys. Rev. Lett. 110, 121803 (2014).

Reprints were made with permission from the publishers.

vii viii Publications not Included in the Thesis

As a member of the ATLAS experiment collaboration, I am co-author of 285 publications not referred to in this thesis (April 29 2015). These papers include detector and performance reports as well as physics analyses using ATLAS data. To become an ATLAS author, it is required that you have contributed to the maintenance or development of the ATLAS detector, work which is crucial for the integrity of the research ﬁndings of the ATLAS. My contributions concerned studies on the trigger system, which are described in this thesis. In general, ideas, knowledge and frameworks are shared between members of ATLAS, which indirectly makes every project at ATLAS a collaboration between all of its members.

ix x Author’s Contribution

The work contained in this thesis corresponds to four years of research work at the ATLAS experiment at the CERN Large Hadron Collider (LHC), as well as non-ATLAS work. The research has resulted in three papers attached to this thesis. My contributions to Paper I and Paper III were also presented in my licentiate thesis. A large collaboration such as ATLAS releases public results in a variety of ways. In common for each approach, rigorous internal review takes place. Results can be released as papers submitted to journals and as so- called conference notes and public plots. The latter two categories often represent research findings which are updates to earlier journal results and it is considered most efficient to release them in this way. Paper I [1] describes the performance of the ATLAS missing transverse energy triggers and has been subject to internal peer-review of the ATLAS experiment. It is published as a conference note. I contributed to the paper with studies of the MET triggers, concerning both trigger efficiency and distributions of trigger variables. Paper II [2] concerns a search for magnetic monopoles and highly electrically charged particles with the ATLAS detector and has been published in Physical Review D. I produced cut flows for signals and data and participated in evaluating and developing the event selection and the background estimation. I was solely responsible for the statistical procedure and for the fiducial regions study where I developed the algorithm for finding the regions. I made large contributions to the event generation and validation, for which I produced both the monopole and HECO single particle samples and the HECO samples with a Drell-Yan-like production model as well as the Drell-Yan spin-1/2 HECO event generation. This covered event generation, detector simulation, reconstruction and digitisation and production of D3PDs (data format designed for analysis). I was responsible for the generation level transverse momentum cuts

xi xii Author’s Contribution which included making and analysing trigger eﬃciencies. I contributed to generating samples for the calculation of systematic uncertainties. Paper III [3] describes a search for magnetic monopoles trapped in polar volcanic rocks and has been peer-reviewed by Physics Review Letters. In this search I was responsible for the calibration of the SQUID magnetometer and for the major part of the data taking.

Katarina Bendtz Stockholm, March 2016 Acknowledgments

Several sources of energy which more or less systematically have contributed positively to the outcome of this thesis have been identiﬁed, see Tabs.1-3. I apologize for any group or individual who might have been left out in this section. The lists do not claim to be complete but merely serve as a representative selection of the most dominant contributions.

Team/ Person(s) Most Significant Specification Association/ Contribution(s) Relationship supervisor D. Milstead supervision, discussions devoted co-supervisor S. Hellman discussions L1 related office room mates O. Lundberg room atmosphere warm O. Bylund support mental Stockholm ATLAS group PhD students chats lunch-time seniors advise skillful KTH ATLAS PhD students G. Ripellino alliance cordial E. Sidebo acquaintanceship amicable CERN colleague G. Palacino collaboration excellent theorist S. Sjörs proof-reading, lecturing QFT HIP analysis group collaboration professional CERN colleague J. Beacham cheer amicable CERN colleague S. Pataraio assistance comitted CERN colleague L. Moneta advise cheerful CERN colleague M. Baak advise statistical predefense comittee J. Edsjö comments valuable C. Finley advise professional P.-E. Tegnér engagement professional ATLAS L1 Calo A. Mincer inspiration professional A. Watson encouragement amicable

Table 1: Overview over work related people who have contributed positively to the outcome of this thesis.

xiii xiv Acknowledgments

Team/ Person(s) Most Significant Specification Association/ Contribution(s) Relationship family F. Bonnevier love, support, food endless family C. Bendtz care, love eternal family C. Bonnevier involvement emotional family C.-G. Ericsson encouragement boundless family T. Bonnevier cheer grandiose family D. Zarins support amiable extended family R. Ström inspiration never-ending extended family K., S. and R. Yoshihara friendship faithful extended family A. Isler affection never-ending

Table 2: Overview over family members who have contributed positively to the outcome of this thesis.

Team/ Person(s) Most Significant Specification Association/ Contribution(s) Relationship friend M. Cegrell support infinite friend L. Johansson friendship considerate friend J. Eriksson frontpage, soul-sharing vital friend A. Ehlde love limitless friend T. Petrushevska devotion perpertual friend J., M. and J. Pearson rendez-vous fantastic friend J. Lundberg affection significant friend M. Tylmad connection spiritual friend A. Sellerholm accord mental friend M. Johanssen affinity intellectual friend J. Ojner¨ care persisting friend A.˚ Hedberg affection continuous friend M. Frankel pact PIA friend J. Cummings understanding mutual friend S. Nohlin connection immaterial friend C. Ohm support IT related friend S. Lee solidarity important friend S. Packalén discussions intellectual friend M. and S. Eketorp friendship SF initiated friend H. Silvander boost moral friend K. Konar cheer optimistic friend F. Paues encouragement emotional friend J. Rundbom radiation positive Rosa Stationen crew exuberance incredible

Table 3: Overview over friends who have contributed positively to the outcome of this thesis. Abbreviations

ATLAS A Toroidal LHC ApparatuS BCID (ATLAS) Bunch Crossing Identification BSM Beyond the Standard Model of particle physics CMS Compact Muon Solenoid CKM Cabibbo-Kobayashi-Maskawa CMM (ATLAS) Common Merger Module CP Charge conjugation and Parity inversion CSC (ATLAS) Cathode Strip Chambers CTP (ATLAS) Central Trigger Processor DAQ (ATLAS) Data Acquisition System DY Drell-Yan EF Event Filter (trigger) EM ElectroMagnetic EM Calo (ATLAS) ElectroMagnetic Calorimeter EM1 First layer of the (ATLAS) ElectroMagnetic (calorimeters) EM2 Second layer of the (ATLAS) ElectroMagnetic (calorimeters) EM2 Third layer of the (ATLAS) ElectroMagnetic (calorimeters) EW ElectroWeak ETH Eidgenössische Technische Hochschule ET Transverse energy EW ElectroWeak interaction FCAL (ATLAS) Forward CALorimeter gD The Dirac charge GR General Relativity GUT Grand Unified Theory HadCore (ATLAS) Hadronic inner Core HIP Highly Ionising Particle HECO Highly Electrically Charged Object HERA Hadron-Electron Ring Accelerator HLT (ATLAS) Highly Level Trigger (L2 and EF) HT (ATLAS) High Threshold (TRT hits) JEM (ATLAS) Jet Energy Module IBL (ATLAS) Insertable B-layer ID (ATLAS) Inner Detector IP (ATLAS) Interaction Point MC Monte Carlo

xv xvi Abbreviations

MoEDAL Monopole and Exotics Detector at the LHC MLE Maximum Likelihood Estimator LAr (ATLAS) Liquid Argon calorimeter LHC The Large Hadron Collider LEP Large Electron-Positron Collider LSB (ATLAS) Layer Sum Boards L1 (ATLAS) Level 1 (trigger) L2 (ATLAS) Level 2 (trigger) LED Large Extra Dimensions LSB Least Signifcant Bit LT (ATLAS) Low Threshold (TRT hits) LUT Look Up Table MDT Monitored Drift Tubes MET Missing ET NIEL Non-Ionising Energy Loss PV (ATLAS) Primary Vertex QM Quantum Mechanics QCD Quantum ChromoDynamics QED Quantum ElectroDynamics QFT Quantum Field Theory RMS Root Mean Square ROB (ATLAS) Read Out Buﬀers ROD (ATLAS) Read Out Drivers RoI Region of Interest (ATLAS L1 trigger) ROS (ATLAS) Read Out System SCT (ATLAS) SemiConductor Tracker SLC Stanford Linear Collider SM The Standard Model of particle physics SMP Stable Massive Particles SP Single Particle (simulation sample) SUSY SUperSYmmetry SQUID A Superconducting Quantum Interference Device TileCal (ATLAS) Tile Calorimeter TOF Time-Of-Flight TTB (ATLAS) Trigger Tower Boards TRT (ATLAS) Transition Radiation Tracker TRT HT (ATLAS) TRT High Threshold TRT LT (ATLAS) TRT Low Threshold XS (ATLAS) MET signiﬁcance Contents

Abstract iii

Publications Included in the Thesis vii

Publications not Included in the Thesis ix

Author’s Contribution xi

Acknowledgments xiii

Abbreviations xv

Contents xvii

Preface1

1 Theory and Previous Research3 1.1 The Standard Model of Particle Physics...... 3 1.2 Physics Beyond the SM...... 16 1.3 Highly Ionising Particles...... 17 1.4 Earlier Searches...... 22

2 Experimental Overview 29 2.1 Particle Physics Experiments...... 29 2.2 The LHC...... 30 2.3 The ATLAS Detector...... 30 2.4 The SQUID Magnetometer and a Monopole Signature.. 50

xvii xviii Contents

3 ATLAS Level1 Trigger Studies 53 3.1 Trigger Eﬃciency and Bootstrapping...... 53 3.2 L1 Single Electron/Photon Triggers...... 55 3.3 Performance of the MET Signiﬁcance Trigger...... 65 3.4 L1 Trigger Upgrade Studies...... 82

4 Highly Ionising Particle Detector Response 89 4.1 HIPs in the ATLAS Detector...... 89 4.2 Energy Deposition...... 89 4.3 δ-ray Production...... 93 4.4 Recombination and HIP Correction to Birks’ Law..... 94 4.5 Magnetic Field Deviation...... 95

5 Search for Magnetic Monopoles and HECOs at ATLAS 97 5.1 Introduction...... 97 5.2 Simulations...... 98 5.3 Event Selection...... 101 5.4 Single Particle Selection Eﬃciency and Fiducial Regions. 113 5.5 Drell-Yan Signal Selection Eﬃciency...... 119 5.6 Systematic Uncertainties...... 120 5.7 Background Estimation...... 123 5.8 Statistical Procedure for Limit Setting...... 129

6 Search for Magnetic Monopoles in Polar Volcanic Rocks 143 6.1 Introduction...... 143

7 Summary and Outlook 151

Svensk sammanfattning 155

References 159 Preface

The field of particle physics has entered a new era in which a large fraction of the experiments are devoted to searching for new physics, rather then confirming the correctness of various predictions of the Standard Model (SM) of particle physics.1 The ATLAS detector at the Large Hadron Collider (LHC) was primarily designed for Higgs and Beyond Standard Model (BSM) searches. Among the most important search observables are stable massive particles (SMP), predicted in many BSM theories. In this context, “stable” refers to being sufficiently long-lived such that the particles do not decay during their passage through the ATLAS detector, that is 100 ns. The term “massive” here means greater than (1 GeV). SMPs are also taken to interact with the detector. This the- O sis concerns the search for SMPs in terms of magnetic monopoles and Highly Electrically Charged Objects (HECOs), i.e. particles with electric charges substantially greater than the elementary charge e. HECOs and monopoles at TeV scale masses have been sought at ATLAS, in collisions with at that time the worlds highest centre-of-mass energy, 8 TeV. This thesis also includes a search for monopoles trapped in polar volcanic rocks.

The thesis is organised as follows. In Chapter 1, the reader is introduced to the theoretical background of the research presented in this thesis. Earlier search results are also discussed. Chapter 2 describes experimental observables and the experimental set-ups used in this thesis. The ATLAS detector at the LHC will be introduced, along with a short introduction to SQUID magnetometers. In Chapter 3, research related to the ATLAS trigger system is presented. In Chapter 4, the interaction of monopoles and HECOs with matter is discussed, in preparation for

1The observation of non-zero neutrino masses (through neutrino oscillation experiments) falsify the SM, where the neutrinos are assumed to be massless.

1 2 Preface

Chapter 5, which covers the search for monopoles and HECOs at the AT- LAS detector. Chapter 6 gives an overview of the search for magnetic monopoles trapped in volcanic rocks. Chapter 7 gives a short summary and outlook.

Natural units i.e. ~ = c = 1 are typically used when describing theoretical topics. Otherwise, units are chosen so as to be appropriate to the context. For example, metres are used as the unit of length when describing the size of the ATLAS detector. Chapter 1

Theory and Previous Research

In this chapter selected theoretical topics relevant to the research presented in this thesis are outlined. A brief overview of earlier research ﬁndings is also given. The chapter begins by introducing the Standard Model (SM) of particle physics, discussing ﬁelds and Lagrangians, and continues with experiments which test the predictions of of the SM. This is followed by a short discussion of theories Beyond the SM (BSM) relating to my research. A section focusing on magnetic monopoles1 closes the chapter.

1.1 The Standard Model of Particle Physics

The SM [4,5,6] describes the properties and interactions of the fundamental particles of nature. The SM includes several Quantum Field Theories (QFTs). Quantum ElectroDynamics (QED) describes the electromagnetic interaction and ElectroWeak (EW) theory combines electromagnetic and weak interactions into one uniﬁed theory. Quantum Chromo Dynam- ics (QCD) describes the strong interaction.

Fundamental Particles and Interactions The SM comprises fermions, which are spin-1/2 particles, and bosons, which are integer-spin particles. For each elementary particle there is a corresponding antiparticle with the same mass but opposite electric charge.

1In this thesis, the term “magnetic monopole”, or just “monopole”, refers to an object carrying only magnetic charge. In general, nothing prevents a magnetic monopole from also carrying non-zero electric charge (a so called dyon).

3 4 Chapter 1. Theory and Previous Research

The fermions and are divided into leptons and quarks, and are listed in Tab. 1.1. All fermions are weakly interacting and the quarks additionally carry strong colour charge. With the exception of neutrinos, fermions are electrically charged and therefore interact electromagnetically. The fermions are divided into three generations, each containing two quarks and two leptons. The first generation contains the building blocks of stable matter. The neutrinos are massless in the SM, in contrast to what has been observed through the phenomenon of neutrino oscillations. Ex- 2 perimental data have only been obtained for the mass differences, ∆mij, between the mass eigenstates νi, (not coinciding with the flavour eigen- 2 −5 2 2 2 states). The ∆m21 is on the order 10 eV [7] and the ∆m13 and ∆m32 are of the order 10−3 eV2 [8,9]. The SM describes three fundamental interactions: the strong interaction, the weak interaction and the electromagnetic (EM) interaction. Each of these interactions are associated with a spin-1 mediator boson, see Tab. 1.2. As will be discussed in some more detail later in this section, the massive SM fermions and bosons acquire their mass from interaction with the spin-0 Higgs boson. In 2012, the ATLAS and CMS experiment discovered a particle consistent with the SM Higgs boson [10, 11] and nu- merous measurements have since then further confirmed the decay properties and parity and spin to agree with the SM predictions [12, 13, 14]. More data are however needed before non-SM Higgs theories can be ruled out. The Higgs mass is measured to be 125 GeV [7]. ∼

Generation I Generation II Generation III Electric charge [e] Quarks (mass [GeV]) up, u charm, c top, t 2 + (2 10−3) (1.28) (173.1) 3 · down, d strange, s beauty, b 1 (45 10−3) (0.95) (4.18) −3 · Leptons (mass [GeV]) electron, e− muon, µ− tau, τ − 1 (5.11 10−4) (0.106) (1.78) − · e neutrino, νe µ neutrino, νµ τ neutrino, ντ 0

Table 1.1: The spin-1/2 particles, fermions, of the SM. The masses are taken from Ref. [7]. 1.1. The Standard Model of Particle Physics 5

νl l νl νl

W ± Z0

d u u u

l l d d

γ g

l l u u Figure 1.1: Feynman diagrams representing examples of processes in the SM. The top diagrams show lepton-quark interactions via the weak interaction. The bottom diagrams show EM lepton scattering and quark interaction via the strong force.

In Fig. 1.1, examples of the SM interactions are shown, represented by Feynman diagrams. A Feynman diagram is a representation of one of several possible processes contributing to a specific interaction, where an interaction is defined by an initial state and a final state, for example e−e− e−e− scattering. A Feynman diagram represents a term in the → expansion of the interaction hamiltonian. The interaction hamiltonian results in a probability amplitude when combined with an initial and final state, as discussed later in this section. The so called coupling constant, √α, of an interaction, is the expansion coefficient of the interaction hamiltonian. The number of vertices, nv, gives the order of perturbation of the specific process represented by the diagram. The bottom left Feynman diagram of Fig. 1.1, would correspond to a second order (nv = 2) expansion term and would thus contribute O(√α2) to the probability amplitude of the e−e− e−e− scattering. The coupling constant is also a measure of → the absolute strength of the interaction and appears in observables as the interaction rate, cross section etc. These observables are proportional to the square of the probability amplitude. The partons of the nucleons are held together by the strong force which acts on objects carrying colour charge. The strong interaction increases with distance up to approximately 1 fm, the size of a hadron, which is a 6 Chapter 1. Theory and Previous Research bound state of quarks. Free quarks have never been observed isolated [7], a phenomenon referred to as colour confinement. At a distance of 1 fm it is ∼ energetically favorable for a new quark-antiquark pair to be produced and hadrons can be formed. This is a typical picture of so called hadronisation used in models [15]. For small distances, the strong force is weak and quarks and gluons in a hadron are to some extent free. This is referred to as asymptotic freedom. At distances & 1 fm, the strong coupling constant, αS, is > 1, which makes the use of perturbation theory to calculate interaction rates impossible, and other techniques have to be used [16]. The weak interaction is short-range, 10−18 m, and its mediator ∼ bosons are massive, m 100 GeV. The mediators, the Z and W bosons, ∼ couple to weakly charged particles, which are all the fermions and also the Z and W bosons themselves. The weak interaction is special in that it violates Charge conjugation and Parity inversion (CP) for hadronic interactions. Charge conjugation invariance means that all interactions involving a set of particles occur at the same rate as the corresponding interactions for the antiparticles. The parity transformation reverses the momentum direction but leaves the spin projection unchanged. Parity invariance implies that a process occurs at the same rate as its mirror image would. CP violation is a consequence of the experimentally verified non-zero phase factors in the CKM matrix [7], which translates from strong force eigenstates to weak force eigenstates for quarks.

Mediator Interaction Charge [e] Mass [GeV] Couples to electro- EM charged photon, γ 0 0 magnetic particles W +,W − +1, 1 80.4 weakly charged weak − Z0 0 91.2 particles gluon, g strong 0 0 strongly charged particles

Table 1.2: The SM interactions and their mediators. The masses are taken from Ref. [7].

The EM interaction is responsible for keeping the atomic nucleus together with the electrons. It is thus as fundamental to the formation of matter 1.1. The Standard Model of Particle Physics 7 as the strong force. The range of the force is infinite and the coupling 2 constant αEM (q ), where q is the momentum transfer in the process, 1 (αEM = 1/137 for q 0) which makes perturbation theory applica- → ble [17]. The interactions - scattering, creation, annihilation - between relativistic particles are described within the framework of QFT. It is a gen- eralisation, consistent with the principles of Quantum Mechanics (QM), of the classical system of particles and fields with which they interact. The particles are interpreted as quanta of continuous fields. More details can be found in Refs. [18, 19, 20]. The ideas of QFT grew out of the need for a quantum version of the classical electromagnetic field with its associated photons. For QED, an obvious starting point was therefore the classical electrodynamic La- grangian field theory which was quantised, and subjected to the canonical commutation relations (bosons) or anticommutation relations (fermions) of QM. For the weak and strong interactions, no classical counterparts exist and a Lagrangian was developed from what is known about the interactions. The theory was then tested against measurements. Any QFT is required to be consistent with the observed symmetries and particles and also to satisfy some theoretical properties:

Gauge invariance: Local phase transformation invariance pre- • serves the currents (charges) of the theory.

Global symmetries: • – Internal symmetries: Global subgroups of gauge groups, for example electric charge. – Space-time symmetries: Lorentz invariance and time-and- space translation.

Technical requirements: • – Locality: The interactions of the Lagrangian density only involves products of ﬁelds at the same point in space, required for causality.

The weak interaction treats left-handed (L) and right-handed (R) leptons L L diﬀerently. The left-handed lepton ﬁelds, ψl and ψνl , are combined into 8 Chapter 1. Theory and Previous Research

L a weak isospin doublet, Ψl (x):

L ! L ψνl (x) Ψl (x) = L (1.1) ψl (x) where the index l denotes any of the three lepton families. The free-field leptonian Lagrangian density, L, is correspondingly written as: L0 L = i[Ψ¯ L(x)∂/ΨL(x) + ψ¯R(x)∂/ψR(x) + ψ¯R(x)∂/ψR(x)] (1.2) L0 l l l l νl νl µ Here ∂/ = γ ∂µ and the ψ¯ denotes the conjugate field of ψ. The weak interaction and its vector bosons are introduced to the lepton field by gauge fields which keep the Lagrangian invariant under local U(1) and µ µ SU(2) gauge transformations. Four gauge fields, B (x) and Wj (x), are introduced by replacing the ordinary derivatives, ∂µ, by covariant derivatives, Dµ:

µ L µ µ 0 µ L D Ψ (x) = [∂ + igτjW (x)/2 ig B (x)/2]Ψ (x) (1.3) l j − l DµψR(x) = [∂µ ig0Bµ(x)]ψR(x) (1.4) l − l µ R µ R D ψνl (x) = ∂ ψνl (x) (1.5) 0 where g and g are coupling constants and the τj are the Pauli matrices. The Lagrangian density now reads:

¯L L R R R R L = i[Ψ (x)D/ Ψ (x) + ψ¯ (x)D/ψ (x) + ψ¯ (x)D/ψ (x)] (1.6) L l l l l νl νl µ where D/ = γ Dµ and L is called the leptonian Lagrangian density, L including both the free-field leptonian Lagrangian density, Eq. 1.2, and an interaction term describing the interactions between the leptons and the gauge bosons. Introducing the non-Hermitian gauge field Wµ(x) (and † its adjoint, Wµ(x)): 1 Wµ(x) = [W1µ(x) iW2µ(x)] (1.7) √2 − and also two Hermitian fields Aµ(x) and Zµ(x) defined as:

W3µ(x) = cos θW Zµ(x) + sin θW Aµ(x) (1.8)

Bµ(x) = sin θW Zµ(x) + cos θW Aµ(x) (1.9) − the Lagrangian density can be written in terms of the ﬁelds representing the weak and EM interactions gauge bosons discussed above. The ﬁelds 1.1. The Standard Model of Particle Physics 9

† ± Wµ(x) and Wµ(x) are the W boson fields, the Zµ(x) field is the Z boson µ field and the A (x) is the photon filed. The θW is referred to as the weak mixing angle. The Lagrangian density is further complemented by the bosonian Lagrangian density, B: L 1 µν 1 † µν 1 µν B = Fµν(x)F (x) F (x)F (x) Zµν(x)Z (x) L − 4 − 2 W µν W − 4 µ ν + gijkWiµ(x)Wjν(x)∂ Wk (x) 1 2 µ ν g ijkilmW (x)W (x)Wlµ(x)Wmν(x) (1.10) − 4 j k where F µν(x) is the electromagnetic field tensor , F µν(x) = ∂νW µ(x) W − ∂µW ν(x) and Zµν(x) = ∂νZµ(x) ∂µZν(x). The first three terms are − the free boson fields and the two last terms represent the bosonic self- interaction, not present in the photon field. In the EW theory so far, the fermions and bosons are massless. Masses are introduced by means of the Higgs mechanism through what is referred to as spontaneous symmetry breaking. Spontaneous breaking of a symmetry of the Lagrangian occurs when this symmetry is broken by the vacuum state. For the Higgs, the non-zero vacuum expectation value of the Higgs field, 0 φ(x) 0 = φ = 0, breaks part of the SM gauge sym- h | | i 0 6 metry, the SU(2) U(1). For a vanishing expectation value, the symmetry ⊗ is preserved. However, this minimum is not stable and the perturbation is naturally done around the true, degenerate minimum, φ0. The Higgs field is represented by a scalar field, ΦH (x), and the Higgs Lagrangian density, H , is given by: L µ † 2 † H (x) =[D Φ(x)] [DµΦ(x)] µ Φ (x)Φ(x) L − λ[Φ†(x)Φ(x)]2 (1.11) − where

µ µ µ 0 µ D Φ(x) =[∂ + igτjWj (x)/2 + ig YB (x)]Φ(x) (1.12) and where Y is the so called weak hypercharge. For µ2 < 0, λ > 0, this results in a vacuum expectation value:

0 φa 0 0 Φ(x) 0 = Φ0 = 0 = (1.13) h | | i φb v/√2

2 1/2 0 0 with v = ( µ /λ) (> 0) and where φa and φb are constants. The last − 0 0 step comes from choosing speciﬁc values for φa and φb corresponding to 10 Chapter 1. Theory and Previous Research the so called unitary gauge. In the unitary gauge Higgs ﬁeld is expanded about the ground state as:

1 0 Φ(x) = (1.14) √2 v + σ(x)

The Higgs ﬁeld interacts with the fermions through what is referred to as the Yukawa coupling described by the Lagrangian density, LH : L L R † R L LH (x) = gl[Ψ¯ (x)ψ (x)Φ(x) + Φ (x)ψ¯ (x)Ψ (x)] L − l l l l L R † R L gν [Ψ¯ (x)ψ (x)Φ(˜ x) + Φ˜ (x)ψ¯ (x)Ψ (x)] (1.15) − l l νl νl l ˜ † T where gl and gνl are coupling constants and Φ(x) = i[Φ τ2] . 2 − The EW Langrangian density , EW , can now be written as a sum L of the leptonian Lagrangian density, L (Eq. 1.6), the gauge-boson La- L grangian density, B (Eq. 1.10), the Higgs Lagrangian density, H (Eq. 1.11), L L and the Yukawa Lagrangian density, LH (Eq. 1.15): L

EW = B + H + L + LH = L L L L L 1 µν FµνF (1.16) − 4 1 F † F µν + m2 W †W µ (1.17) − 2 W µν W W µ 1 µν 1 2 µ ZµνZ + m ZµZ (1.18) − 4 2 Z 1 µ 1 2 2 + (∂ σ)(∂µσ) m σ (1.19) 2 − 2 H + ψ¯l(i∂/ ml)ψl + ψ¯ν (i∂/ mν )ψν (1.20) − l − l l + I L where I represents all interaction terms of the Lagrangian density. New L †µ µ µ µ mass terms have emerged for the ψl, W , W , Z , but not for the A ﬁeld. This is consistent with observations, a massless photon and massive ± fermions and W and Z bosons! The SM assumes mνl = 0 and no right- handed neutrinos are assumed to exist. Non-zero neutrino masses are however observed as will be discussed later in this section. There is also a mass term for the Higgs ﬁeld, indicating that the Higgs boson is massive.

2The full SM EW Lagrangian density also includes couplings to strong color charged ﬁelds, not discussed in this thesis. 1.1. The Standard Model of Particle Physics 11

Eq. 1.19 is the Klein-Gordon Lagrangian density and describes the spin-0

Higgs ﬁeld. The mass parameters mW , mZ , mH , ml, mνl deﬁned as:

1 p 2 mW = vg, mZ = mW /cosθW , mH = 2µ (1.21) 2 − √ √ ml = vgl/ 2, mνl = vgνl / 2 (1.22)

The masses all free parameters of the SM to be determined by measurements. The transition amplitude of a specific interaction, such as the annihilation and creation of particles arising in particle collisions is a non- trivial problem. It amounts to solving the Schroedinger equation for a time-dependent state vector, φ(t) , for the interaction part, H , of the | i I Hamiltonian: d i φ(t) = H (t) φ(t) (1.23) dt | i I | i where the system is expressed in the interaction picture. The S matrix represents the time evolution of a state involved in an interaction: φ(t = ) = S φ(t = ) . The probability amplitude for a specific | ∞ i | −∞ i final state, f = φ(t = ) , resulting from a given initial state, i = | i | ∞ i | i φ(t = ) , is: | −∞ i

f S i = Sfi (1.24) h | | i The S matrix is calculated by solving Eq. 1.23: Z t Φ(t) = i + ( i) dt1HI(t1) φ(t1) (1.25) | i | i − −∞ | i which can only be done iteratively. This leads to the Dyson expansion when t : → ∞ ∞ n Z ∞ Z ∞ X ( i) 4 4 4 S = − ... d x d x . . . d xnT I (x ) I (x ) ... I (xn) n! 1 2 {H 1 H 2 H } n=0 −∞ −∞ (1.26) where I is the Hamiltonian interaction density used in QFT and the H integrals accordingly are taken over all space. The T ... is the time- { } ordered product, i.e. later times stand to the left of earlier times and all boson (fermion) fields are treated as though their (anti-)commutators 12 Chapter 1. Theory and Previous Research vanish. This is a power series in the coupling constant of the theory. The terms in Eq. 1.26 describe all the possible processes given the interaction I , each order corresponding to more and more complicated H processes including creation and absorption of virtual particles. The ma- (n) trix element, Sfi , gives the probability amplitude for the given order, n, of perturbation. For most practical uses, the two leading orders are used. The cross section for a specific process is obtained by expressing the matrix element in momentum space, fixing the volume to the scattering centre and integrating over momentum space. The momentum space is reduced to what is allowed by the conservation of momentum and the final state momenta are not all independent variables. The size of the allowed momentum space is often one of the largest contributions to the cross section.

Experimental Tests of the Standard Model The SM has been subject to a large number of tests at many diﬀerent experiments and has in many cases been tested to a great precision. Such measurements have been carried out at colliders eg. LEP and SLC [21], HERA [22], the Tevatron [23] and the LHC [24], and in non-collider work [25]. Three such tests are described below.

Electron Magnetic Moment The SM, and in particular QED, has been experimentally veriﬁed to an accuracy of 1 part in 1012 [26,7] by measurements of the electron spin magnetic dipole moment, ~µ:

~µ = gµBS~ (1.27) − where µB = e/(2me), me is the electron mass, S~ is the electron spin angular momentum. For the electron, g/2 = 1, if not allowing for interactions with the vacuum. Deviations from 1 therefore probe these corrections. The theoretical value of this quantity is [26]: g theo = 1.00115965218113(86) (1.28) 2 and the experimental value is [26]:

gexp = 1.00115965218073(28) (1.29) 2 1.1. The Standard Model of Particle Physics 13 where the uncertainties are given inside the brackets. The agreement between experimental result and the prediction is impressive.

The Running of the Strong Coupling Constant αS

The strong coupling constant, αS, is an eﬀective coupling constant. As part of the renormalisation procedure, the divergent contributions associated with higher order quark loop and gluon self-interactions are absorbed into an eﬀective charge or coupling constant. This coupling constant then depends strongly on Q, the momentum scale of a given interaction. The quark loops contribute positively to the value of αS as a function of Q, and the gluon loops negatively, leading to an overall decrease in the coupling constant as a function of Q [17].

Sept. 2013 τ decays (N3LO) αs(Q) Lattice QCD (NNLO) DIS jets (NLO) Heavy Quarkonia (NLO) 0.3 – e+e jets & shapes (res. NNLO) Z pole fit (N 3LO) (–) pp –> jets (NLO) 0.2

0.1 QCD αs(Mz) = 0.1185 ± 0.0006 1 10 100 1000 Q [GeV]

Figure 1.2: Measurements of the strong coupling constant αS as a function of the momentum scale Q. In brackets are the order of perturbation theory used in the extraction of αS. The ﬁgure is taken from Ref. [7].

Precision measurements of αS have been performed, for example with the hadronic decay of the tau lepton, jet production rates in e−e+ annihilation, the observed spectra of heavy quarks and deep inelastic scattering [7] and the results are summarised in Fig. 1.2. The running of 14 Chapter 1. Theory and Previous Research the coupling constant predicted by theory using data taken at the world average measurement of the Z mass, is also shown and agrees with the individual measurements at diﬀerent scales.

ElectroWeak SM Fits

There are many free parameters of the SM, for example the particle masses, the coupling constants, and the widths of the weak interaction gauge bosons. These need to be measured in order to determine their values. Many of these parameters are also related to each other theoretically. Several independent precision measurements of the parameters and their associated uncertainties can therefore be combined to determine a set of parameters by multidimensional fits, so called EW fits. This method has also been used to validate the consistency between experimental results and theoretical predictions [27]. In Fig. 1.3 examples of the results (blue, grey) from EW fits for MW , the W boson mass and mt, the top quark mass, are given. The experimental values of MW and mt are given as well (green bands). The fit results show a striking agreement with the direct measurements, visible in the overlap of the region defined by the blue and grey contours on one hand, with the region defined by the green contours on the other hand. In addition, both the fit result without the Higgs mass, MH , measurement and the direct measurements of the W mass and top quark mass are consistent with the observed Higgs mass of 125 GeV. ∼ Missing Pieces Appealing for New Theories

Despite the great success of the SM, there are however strong indications of it simply being an eﬀective theory at lower energy scales. One of the most important manifestations of this is the fact that gravity is not included in the SM, and that there is an energy scale, the Planck scale of order 1019 GeV, at which gravity cannot be neglected in order to describe a system. QM and Heisenberg’s uncertainty relation, ∆x∆p = 1/2, predicts that the higher the energy of a photon directed towards an electron to measure its position, the better the position can be determined since the energy uncertainty of the system increases. As discussed in the previous section, QFT introduces the possibility of creation and annihilation of particles and thus puts a limit on how well we can localise the particle. When the energy of the incoming photon is larger than than (2me), O then a new electron-positron pair can be produced, and the position of the 1.1. The Standard Model of Particle Physics 15

m world comb. ± 1σ 68% and 95% CL contours t mt = 173.34 GeV fit w/o M and m measurements σ = 0.76 GeV [GeV] 80.5 W t σ ⊕ W = 0.76 0.50 GeV fit w/o M , m and M measurements theo W t H M direct MW and mt measurements 80.45

80.4

± σ MW world comb. 1 ± 80.35 MW = 80.385 0.015 GeV

80.3

80.25 = 50 GeV = 125.14 GeV = 300 GeV = 600 GeV M H M H M H M H

140 150 160 170 180 190

mt [GeV]

Figure 1.3: Contours at 68% and 95% CL obtained from scans of the mass of the W boson, MW , versus the mass of the top quark, mt, as compared to the direct measurements. A theoretical uncertainty of 0.5 GeV is added to the direct top mass measurement. The Higgs mass, mH , is related to the MW and mt as is also marked in the ﬁgure. The graph is from Ref. [27].

first electron is not well-defined anymore. The corresponding limit on the photon wavelength for determining the position of an arbitrary particle of mass m, is referred to as the Compton wavelength, λCompton,m = 1/(m), which then is of the same scale as the minimum uncertainty in position of the particle. The λCompton,m thus sets the cut-off at which QFT becomes important. The Planck mass of a particle corresponds to the mass at which the λCompton,m coincides with the Schwarzchild radius, rs(m), the radius of an object of mass m below which the density of mass is so high as to create a black hole. The Planck mass thus represents the energy scale at which QFT certainly has to take General Relativity (GR) and gravity into account. It is problematic to unite GR describing a curved space-time and QFT. The Planck scale therefore indicates where the SM must break down, if not before, and at which new physics processes must emerge. 16 Chapter 1. Theory and Previous Research

In the SM, the observable Higgs mass has two contributions, the so- called bare mass and a term arising from radiative corrections. If the renormalisation cut-off is taken as the Planck scale, and thus the bare mass includes corrections from higher energy scales than the Planck scale, then both contributions are on the order of 1033 and perfectly cancel to give the observable Higgs mass on the order of 100 GeV. This is by some regarded as an improbable fine-tuning since it would be expected that the physics processes below and above the cut-off would not be closely related [28, 29]. Another striking piece of evidence showing the incompleteness of the SM is the existence of so called dark matter. Observations of the rota- tional patterns of galaxies and clusters of galaxies, suggest either that there are regions of the Universe where the laws of gravity do not hold, or that there are additional distributions of matter invisible to our instru- ments [30]. This proposed matter, dark matter, is estimated to make out 26.8% of the energy and matter in the Universe, where only 4.9% is ordinary matter and the rest is so called dark energy [31]. The SM does not include particles which can account for the observed dark matter [32]. Further, neutrino oscillations would not be possible were the neutrinos massless, assumed in the SM. The oscillation refers to a change from one generation to another and is a consequence of the generation eigenstates not being mass eigenstates. It has been experimentally observed in a number of experiments [33, 34]. Finally, the SM does not provide any explanation for electric charge quantisation and thus the apparently identical values of, e.g. electron and proton electric charge [35]. As this is such a fundamental observation of particle properties, the absence of a theoretical foundation of this assumption is regarded as a serious shortcoming of the SM and is directly relevant to the work in this thesis. Dirac addressed this issue by introducing magnetic monopole charges, as is described in Sec. 1.3. It is also addressed in Grand Unified Theories (GUT) (see Sec. 1.2)[36].

1.2 Physics Beyond the SM

As discussed in the previous section, new theories Beyond the SM (BSM) are needed in order to fully describe the phenomena observed in nature. One of the most popular is the Supersymmetry (SUSY) framework, which gives rise to a number of diﬀerent models [37]. SUSY postulates a new 1.3. Highly Ionising Particles 17 quantum number, R-parity, a multiplicative symmetry where SUSY particles have odd R-parity and SM particles have even R-parity. SUSY models address the ﬁne-tuning problem discussed above by introducing a new set of particles, supersymmetric partners to the SM particles, resulting in the cancellation of the large corrections to the Higgs mass. Furthermore, R-parity conserving SUSY models also provide a dark matter candidate.

Theories of Large Extra Dimensions (LED) [38, 39], introduce one or several additional dimensions in which gravity can propagate. This allows for a much stronger gravity coupling than the 4-dimensional eﬀective coupling that is observed, meaning that the Planck scale can be reduced. For example for an extra dimension of size 1 mm, the Planck scale is reduced to the TeV scale. In the framework of some models of LED, black holes could be produced at TeV scale energies, referred to as micro-black holes. They would instantly decay and the so called micro-black hole remnants could possibly be observed in a particle detector.

In GUT theories the electroweak and strong interactions are uniﬁed at high energies, typically at the GUT scale, 1015 GeV. The uniﬁcation is brought about by one large gauge symmetry represented by a symmetry group, G(X), containing the other gauge interaction symmetry groups: G(X) SU(3) SU(2) U(1) [7]. ⊃ ⊗ ⊗

1.3 Highly Ionising Particles

Magnetic Monopoles

Magnetic monopoles are objects with an isolated magnetic charge, in analogy with the electric charge. Introducing magnetic monopoles into the SM renders Maxwell’s equations symmetric and addresses charge quantisation, as will be explained below. The equations in the following two sections are expressed in SI units. 18 Chapter 1. Theory and Previous Research

Maxwell’s Equations The classical description of an electrodynamical system is represented by the Maxwell equations: ρ E~ = e (1.30) ∇ · ε0 B~ = 0 (1.31) ∇ · ∂B~ E~ = (1.32) ∇ × − ∂t ! ∂E~ B~ = µ ~j + ε (1.33) ∇ × 0 e 0 ∂t where B~ and E~ are the magnetic and electric ﬁeld, respectively. The ρe represents the electric charge density and ~je is the electric current. The parameters ε0 and µ0 are the vacuum permittivity and vacuum perme- ability, respectively. Assuming that the magnetic densities satisfy the same form of the continuity equation as the electric densities, magnetic charge and current densities can be introduced and Eq. 1.31 and Eq. 1.33 would become: B~ = µ ρ (1.34) ∇ · 0 m ∂B~ E~ = µ ~j (1.35) ∇ × − ∂t − 0 m

The ρm and J~m parameters are the magnetic charge density and magnetic current, respectively. Eq. 1.30, Gauss’ law for electric charges, relates an electric charge density to an electric field. Eq. 1.34 gives an equivalent equation for magnetic charges. In analogy with Ampere’s law, Eq. 1.33, Faraday’s law, Eq. 1.32, which gives how changing magnetic fields produce electric fields, is adjusted by the addition of a magnetic current, as is presented in Eq. 1.35. For the following duality transformation [40, 41]: E~ 0 = E~ cos α + cB~ sin α (1.36) cB~ 0 = cB~ cos α E~ sin α (1.37) − and the corresponding transformation of the sources, 0 cρe = cρe cos α + ρm sin α (1.38) ρ0 = ρ cos α cρ sin α (1.39) m m − e the generalized Maxwell equations are invariant under the rotation by α, where α is a real number. The distinction between electric and magnetic 1.3. Highly Ionising Particles 19 charges, electric and magnetic fields, is thus arbitrary with regards to the laws of nature. By convention α = 0 is taken. Therefore when a monopole is discussed in the context of a search, what is really meant is that a new particle with a different magnetic charge to electric charge ratio to the SM particles is sought. The Lorentz force law is accordingly modified to include the electromagnetic force on a magnetic charge qm:

1 F~ = q E~ + ~v B~ = F~ = q E~ + ~v B~ + q B~ ~v E~ (1.40) e × ⇒ e × m − c2 ×

The modiﬁed Faraday’s law and the Lorenz force law allow searches for monopoles with the induction method (see Chap.6) and via a signature of a particle being accelerated along a magnetic ﬁeld.

Dirac Charge Quantisation and the Dirac Charge

Dirac showed that magnetic monopoles can be accommodated into the existing theories of electromagnetism and quantum mechanics [42, 43]. In this section, a modiﬁed version of his argument is presented. The magnetic ﬁeld B~ for a monopole is obtained from Gauss’ law for monopoles, Eq. 1.34:

µ grˆ B~ = 0 (1.41) 4πr2 where g is the magnetic charge of the monopole and where the magnetic field is radial in analogy with the electric field from an electric charge. In order to be consistent with electromagnetism, there has to be a magnetic potential, A~, satisfying B~ = A~. This is satisfied for the following ∇ × magnetic potential:

µ g(1 cos θ) A~ = 0 − φˆ (1.42) 4πr sin θ where the θ is the polar angle and φ the azimuthal angle and spherical polar coordinates are used, see Fig. 1.4. There is however a singularity at θ = π. Using the gauge freedom of electrodynamics, this can be solved 20 Chapter 1. Theory and Previous Research

θ"

φ" gD# B"

Figure 1.4: Schematic overview of the polar coordinate angles θ and φ π and the boundary B at θ = used in the path integrals Eq. 1.45 and 2 Eq. 1.46. The magnetic monopole is marked as g.

by introducing two diﬀerent potentials for the two diﬀerent hemispheres around a monopole:

 µ g(1−cos θ) 0 φˆ 0 θ π  4πr sin θ ≤ ≤ 2 A~ = (1.43)  −µ g(1+cos θ)  0 φˆ π θ π 4πr sin θ 2 ≤ ≤ where both satisfy B~ = A~ and no singularities exist. From the ∇ × quantum mechanical perspective, it is the vector potential A~ that is the observable, (and not B~ ), changing the phase of the wave function of an electrically charged particle, ψ ψi∆φ. The phase shift, ∆φ, of a particle → with electric charge q following a path P , is given by :

q Z ∆φ = A~ d~l (1.44) ~ P ·

It therefore needs to be verified that the two potentials in Eq. 1.43 give the same measurable effect on a particle traveling around the boundary π B, θ = 2 , see Fig. 1.4. This implies that the difference in phase change, 1.3. Highly Ionising Particles 21

∆φupper ∆φlower between the two path integrals at B is required to be − a multiple of 2π: Z Z µ g(1 cos π ) q ~ ~ q 0 2 qµ0g ∆φupper = A dl = − π rdφ = (1.45) ~ B · ~ B 4πr sin 2 2~ Z Z µ g(1 + cos π ) q ~ ~ q 0 2 qµ0g ∆φlower = A dl = − π rdφ = (1.46) ~ B · ~ B 4πr sin 2 − 2~ qµ0g nh ∆φupper ∆φlower = = 2πn q = (1.47) − ~ → gµ0 This results in a charge quantisation condition with interesting conse- quences. If there is one type of magnetic charge in the Universe (i.e. g is constant) then electric charge quantisation is explained as a consequence of quantum mechanics. Very few theories address the charge quantisation problem of the SM. If the elementary charge e is taken to be the fundamental charge, Eq. 1.47 states that the magnetic elementary charge (n = 1) is given by: h gD = (1.48) eµ0 where gD is referred to as the Dirac charge. Other charges are conceivable. Assuming for example the down quark to carry the fundamental electric charge results in a minimum magnetic charge of 3 gD. The quantity gD is however widely utilised as a unit of magnetic charge and will be used as such in this thesis. It is worth noticing that the electromagnetic properties of a monopole with charge 1 gD is roughly equivalent to an electrically charged particle with charge 68 e, meaning that a monopole is strongly ionising, a signature which is used in the search described in Chap.4. In analogy with the electric case, the coupling constant for magnetic charges would be: 2 gD αm = 34 (1.49) 4πµ0~c ∼

The coupling αm is thus too large as to allow a perturbative expansion, and estimations of monopole production cross sections are diﬃcult to carry out.

Magnetic Monopoles in BSM Theories Magnetic Monopoles arise naturally in GUT theories with spontaneous gauge symmetry breaking, typically with masses of around 1015 GeV [44, 22 Chapter 1. Theory and Previous Research

45]. However, there are scenarios in which lower mass monopoles, (104) GeV, O are allowed [46, 47, 48]. A recent proposed EW extension to the SM predicts monopoles with masses < 5.5 TeV [49].

Highly Electrically Charged Objects

Highly Electrically Charged Objects (HECOs) are deﬁned in terms of experimental observables as massive (> 100 GeV), long-lived objects with high electric charge ( e). In general, searches for HECOs do not assume any theoretical model and they are regarded as a ”blue skies” search in this thesis. Examples of proposed objects in the literature are however Q-balls [50, 51], strangelets [52] and micro-black hole remnants [53]. HECOs suﬀer from the same problem as monopoles with respect to the non-perturbative nature of the coupling constant.

1.4 Earlier Searches

Magnetic Monopoles and HECOs have previously been sought in both collider [36] and non-collider [54] experiments. In colliders, a common search technique is via measurements of the ionisation energy loss dE/dx as a function of speed using calorimeters and tracking chambers. The energy loss as a function of speed depends on the mass and charge of a particle as is discussed in Chap.4. The tracking chambers are used to measure the curvature of the particle, which is a function of its mass, speed and charge. Combining the two measurements and comparing to simulations, the mass and charge of the particle can be inferred. Ref. [55] describes a search using this method. The particles can alternatively be detected by ionisation damage to plastic foils placed for example around the beam pipe. Examples of searches using this technique are found in Refs. [56, 57, 58, 59, 55]. The low velocity of massive particles with respect to relativistic particles can also be employed as a detection method by direct time-of-flight (TOF) measurements, see Refs. [60, 61]. In addition to the aforementioned techniques, which are applicable to both HECOs and monopoles, there are two methods used to search for monopoles only. The parabolic track that monopoles will follow in the s-z-plane, where z points along the magnetic field (often in the beam direction) and s is the total distance travelled, can be used as a discriminating signal, see Refs. [62, 63]. Due to its very large ionisation rate, a 1.4. Earlier Searches 23 monopole with low velocity may stop soon after its production and then bind to the atoms in the detector material. A second approach is therefore to search for monopoles trapped in material close to the interaction point. The monopole can thereafter be detected using a SQUID apparatus, see Sec. 2.4. This was the procedure for the search for monopoles using the MoEDAL detector, see Ref. [64]. Previous collider searches have been performed at e+e−, lepton-hadron and hadron-hadron colliders and the results are summarised in Tab. 1.3. The mass sensitivity extends up to 1.5 TeV and the charge sensitivity is 24 gD for monopoles and < 240 e for HECOs. Many monopole searches ≤ are also sensitive to HECOs (1 gD 68 e) but this is not always exploited ∼ in the data analysis and HECO limits are not always quoted. The only collider searches quoting limits of HECOs with charges > 2 e is Ref. [65]. Ref. [66] was designed mainly for particles with magnetic charges and provides a 95% CL limit of 70 pb on the cross section limits in a mass range of 1- 45 GeV for 1 gD monopoles, and only quote the sensitivity for HECOs, which is . 240 e. Collider searches for massive particles with charges < 2 e are given in Ref. [36]. The searches presented in Tab. 1.3 and Ref. [66] are all generic searches where no underlying theoretical production model is assumed other than values of mass, electric or magnetic charge and spin.3 Monopoles and HECOs have in addition to collider experiments been sought in cosmic rays and as objects bound in matter [54]. A summary of matter searches are given in Tab. 1.4 where it can be seen that a variety of materials have been examined. These works are comparable to the search described in Chap.6. They assume that stopped monopoles would become bound to an atomic nucleus. Binding calculations have been carried out in for example Ref. [67]. Most of these searches use the induction technique (see Sec. 2.4). The searches for monopoles that are assumed to have stopped in matter include the possibility of monopoles having stopped in the ocean bottom [68] and Moon rocks [69]. The results of these searches were also interpreted within a cosmic ray hypothesis. Cosmic ray searches do not form part of the research in the thesis and little emphasis is therefore placed on them here. Owing to difficulties in calculating monopole interactions, no straightforward connection can be made between the results of different types of searches (collider, cosmic ray, and matter). The cosmic ray searches listed in Tab. 1.5 are given to

3It should be noted that any quoted mass limit assumes a speciﬁc production model, and mass limits are thus not presented in this section. 24 Chapter 1. Theory and Previous Research demonstrate the breadth of the monopole search program. As seen in this table, the typical techniques are Cerenkov and nuclear track detectors. No reproducible evidence for the existence of HECOs or monopoles has been found in either collider, matter or cosmic ray searches. 1.4. Earlier Searches 25

√ s Collision Experiment Mass Charge Charge Cross Ref. [GeV] sensitivity [gD] [e] section [GeV] limit [pb] 1960 pp¯ CDF 100-900 1 - 0.2 [55] 1800 pp¯ E882 - 1 - 0.6 [70, 71] 2 - 0.2 3 - 0.07 6 - 0.2 1800 pp¯ M. Bertani et al. < 850 > 0.5 - 200 [72] 56 pp Hoﬀmann et al. < 30 0.3-3 - 0.1 [73] 63 pp Carrigan et al. < 30 0.2-1.2 - 0.13 [74] 1.2-24 - 0.4 3 7000 pp ATLAS < 1500 1 - 2 × 10− [75] 7000 pp ATLAS 200 - 1000 6 - 17 1-12 [65] 6 25-28 pN Carrigan et al. < 13 0.03-24 - 5 × 10− [76, 77] 300 ep H1 < 140 1 - 2.2 [78] 2 - 0.18 3 - 0.07 6 - 0.04 + 88-94 e e− J.L. Pinfold et al. < 45 1 - 0.3 [79] < 41.6 2 - 0.3 + 89-93 e e− MODAL < 44.9 1 < 240 70 [66] + 34 e e− P. Musset et al. < 16 0.98-5.9 - 0.04 [80] + 29 e e− D. Fryberger et al. 0.29-2.9 < 14 - 0.03 [58, 81] + 35 e e− TASSO ≤ 17 0.15 - 4 [63] 0.44 - 0.04 1 - 0.08 + 10.6 e e− CLEO < 5 0.03 - 0.8 [62] 0.07 - 0.24 0.12 - 1.6

Table 1.3: A summary of selected collider searches for HIPs. The centre- of-mass energy is denoted as √s and the symbol “-” denotes that an experiment did not explicitly quote an acceptance region. The table is from Ref. [36], with the additions of the searches described in Ref. [75] and in Ref. [65]. The electric charge quoted for Ref. [66] corresponds to the sensitivity of the search. 26 Chapter 1. Theory and Previous Research

Technique Material Charge Density Ref. [gD] limit 1 [g− ] 6 induction meteorites and other > 1/3 < 6.9 × 10− [82] 7 induction Fe ore > 0.6 < 2 × 10− [83] 6 induction deep schist > 0.5 < 4.6 × 10− [84] 6 induction manganese nodules > 0.5 < 1.6 × 10− [84] 6 induction seawater > 0.5 < 1.3 × 10− [84] 1 induction 11 materials > 0.04 < 5 × 10− [85] 4 induction Moon rock > 0.05 < 2 × 10− [69] 7 scintillation deep-sea sediment < 140 < 6 × 10− [68]

Table 1.4: Overview over searches for monopoles in matter. The limits are given as density per gram of the examined material. The table is taken from Ref. [7]. 1.4. Earlier Searches 27

2 1 1 Technique Location Velocity range Limit (cm− sr− s− ) 13 induction sea level all β 2·10− 4 16 scintillator underground 10− < β < 0.1 2.5·10− 14 0.1 < β < 0.5 1.3·10− 13 0.5 < β < 1 1.3·10− 4 3 13 sea level 3 · 10− < β < 10− 7.8·10− 3 13 10− < β < 0.5 2.9·10− 4 3 12 plastic streamer tube underground 10− < β < 2 · 10− 4.6·10− 4 3 16 gaseous detector underground 10− < β < 5 · 10− 2.8·10− 3 15 5 · 10− < β < 1 6·10− 4 14 sea level 10− < β < 1 1.4·10− 5 4 16 nuclear-track detector underground 2 · 10− < β < 2 · 10− 3·10− 3 16 2 · 10− < β < 0.02 2·10− 16 0.02 < β < 1 10− 15 sea level 0.04 < β < 1 5.2·10− 5 4 14 high altitude 3 · 10− < β < 2 · 10− 3·10− 16 0.03 < β < 1 6.5·10− 4 20 ancient mica 4 · 10− < β < 0.5 5.5 · 10− 20 γ > 2000 5.5 · 10− 17 Cherenkov light deep water/ice 0.6 < β < 0.8 5·10− 18 0.8 < β < 1 2.3·10− 7 13 19 Cherenkov radio South Pole 10 < γ < 10 2·10− 5 2 16 nucleon decay underground 10− < β < 10− 10− 3 17 deep ice β ∼ 10− 10− 4 12 sea level 5 · 10− < β < 0.05 3·10− 2 in the Sun β < 0.1 6 · 10 24 β − 10−3 23 old neutron stars galaxy all initial β 10− 16 collection (air) sea level stop in atmosphere 4.1 · 10− 15 magnetic field survival galaxy all β 10− 33 galactic seed all β 1.2 · 10− M β . · 4 β mass density Universe all 5 4 10 M Table 1.5: Summary of combined flux limits for cosmic ray monopoles with charges gD that would reach the detector and possess a velocity ≥ in the given range. The table is from Ref. [54], where the specific assumptions needed for the limits to be valid along with the references to the searches are given. 28 Chapter 2

Experimental Overview

This chapter is intended as an overview of the detectors used for this thesis; the purpose is to prepare the reader for the discussion of the techniques and results given in subsequent chapters. At the beginning of this chapter, particle physics experiments in general and the ATLAS detector at the LHC in particular are discussed. The detector will be reviewed from the perspective of the particles studied in this thesis or of my technical studies, and emphasis is placed on the detector components and systems relevant to the research in this thesis. Finally, a brief description of how a SQUID magnetometer can be used to search for monopoles is given.

2.1 Particle Physics Experiments

Particle physics experiments use two main sources of high energy particles [32]. Electrically charged cosmic rays are largely high-energy protons and alpha particles emitted by the Sun or originating from outside the Solar system. By interacting with the atmosphere of the Earth, these create so called secondary rays of lighter particles such pions and muons that can be studied by particle detectors at the Earth [86]. Highly energetic neutrinos originating from distant cosmological objects and reaching the Earth without interacting with the atmosphere are also studied [86]. As an alternative to cosmic rays, high-energy particles may be created by means of accelerating and colliding particles such as protons or electrons. The produced particles are then detected directly after their creation. Particle physics experiments can also be made at low energy scales via, eg, precision measurements of particle properties and the search for stopped exotic objects in matter [25].

29 30 Chapter 2. Experimental Overview

2.2 The LHC

The Large Hadron Collider (LHC), located at CERN, is the world’s largest and most powerful particle collider, installed in a 27 km long tunnel 100 meters under ground. Protons are prepared into so called bunches, accelerated and then made to collide a number of interaction points. During 2012 LHC was operating at 8 TeV centre of mass energy and at an instantaneous luminosity of 1033 cm−2s−1. There are four large experiments at the LHC: ATLAS [87, 88], CMS [89], ALICE [90] and LHCb [91]. The ATLAS and CMS experiments have the broadest physics programs and use general-purpose detectors. The AL- ICE and LHCb physics programs are focused, albeit not exclusively, on heavy ion and ﬂavour physics, respectively. In addition to these, the LHC is also home to three smaller experiments: Totem [92], LHCf [93] and Moedal [94]. Totem and LHCf focus on “forward” physics i.e. particles measured at small angles. Moedal is a dedicated experiment to look for monopoles and other exotic particles. A discussion of its capabilities compared with the work in this thesis is given in Chap.7. The ATLAS detector is described in Sec. 2.3.

2.3 The ATLAS Detector

As one of the two giant multi-purpose detectors at the LHC, ATLAS has been providing all sorts of SM and BSM analyses with data, the most famous one being the search for the Higgs boson [10], resulting in a discovery of a Higgs-like boson the summer of 2012. The detector weighs 7000 tons and extends 45 m in length and 25 m in diameter. The geometry is cylindrical, with the beam pipe at its longitudinal centre axis, and subdetectors covering diﬀerent radial ranges, see Fig. 2.1. Moving outwards from the beam pipe, the Inner Detector (ID) is a tracker, submerged in a 2 T solenoid magnetic ﬁeld. Next are the calorimeters, designed for detecting electrons and photons, as well as heavier hadrons. The muon system is the outermost subsystem, and has its own magnet system to be able to measure the momenta of the muons. The coordinate system and the detector subsystems are described in the following sections.

The ATLAS Coordinate System The ATLAS detector has two coordinate systems with the nominal interaction point (IP), deﬁned as the origin. In the Cartesian right-handed 2.3. The ATLAS Detector 31

Figure 2.1: A cut-away view of the ATLAS detector with its main subsystems. The ﬁgure is from Ref. [87]

coordinate system, the positive direction of the x-axis is defined as pointing from the IP towards the centre of the LHC ring. The positive direction of y-axis is pointing upwards, and the z-axis is parallel to the beam pipe. p In the polar coordinate system, the radius, R = x2 + y2 and φ is the azimuthal angle in the x-y plane, starting from the positive x axis. The angle θ is the angle towards the z axis. The pseudorapidity, denoted as η, is then defined as: θ η = ln tan( ) (2.1) − 2 Along the y and x axes, the pseudorapidity is zero, and parallel to the beam axis it is infinite.

Transverse Energy and Transverse Momentum The transverse plane is deﬁned as perpendicular to the beam axis of a collider experiment. In this plane the total momentum of the system is zero. Particles that do not interact with the detector, and otherwise would be undetectable, will leave a trace as a momentum imbalance in the transverse plane. 32 Chapter 2. Experimental Overview

The momentum in the transverse plane, pT , is also interesting from the perspective that high pT particles are associated with collisions where a lot of energy has been redistributed in order to change the direction of the particles. Collisions where a lot of energy is involved is of course particularly interesting. The pT of an object in ATLAS is defined as the momentum of a particle in the transverse plane, p sin(θ), where θ is · the angle between the particle direction and the beam axis, and p is the momentum of the particle. Particle masses in ATLAS events are typically on the order of the pion mass, 140MeV, and for high energy events, the mass can be neglected ∼ in comparison to the kinetic energy. The measured energy can therefore be taken as a good approximation of the momentum, allowing the construction of vector-like quantities of the energy deposition. The estimated energy of an object, projected on the transverse plane is referred to ET , and the definition used in ATLAS at different levels of reconstruction is given later in this section.

ATLAS Subdetectors The Inner Detector To obtain precision measurements of the momenta and positions of the tracks close to the IP, the ID, see Fig. 2.2, provides a high granularity track reconstruction inside the magnetic ﬁeld directed along the beam pipe. The curvature of the track is used for calculating the momentum and from intersecting tracks, so called vertices, corresponding to particle interactions and decays, are reconstructed. The ID has a diameter of 1.15 m and a length of 5.5 m and covers η < 2.5. It is composed of | | three diﬀerent subsystems, the Pixel detector, the Semiconductor Tracker (SCT) and the Transition Radiation Tracker (TRT), described in the paragraphs below. Since 2014, a fourth subdetector, the Insertable B- layer (IBL) is installed closest to the beam pipe to ensure the tracking robustness at high luminosities. The IBL was not in use by the time of the data taking relevant to this thesis. The relative track momentum resolution deteriorates with increasing momentum, but is also dependent on the pseudorapidity because of the increasing amount of non-active material traversed at large values. The resolution is given by σ 0.05% pT [GeV ] 1% (2.2) pT ∼ · ⊕ 2.3. The ATLAS Detector 33

Figure 2.2: A schematic drawing of a φ slice of the ATLAS Inner Detector. The recently installed IBL layer is omitted from this ﬁgure. A red line shows the track of a charged particle. The ﬁgure is from Ref. [87].

where the σ is the uncertainty of the pT . More information about the ID can be found in Refs. [87, 95, 96, 97, 98]. The standard track reconstruction algorithms or ATLAS make use of all ID subsystems. For HIPs, only the TRT response is well studied and the standard particle identiﬁcations do not apply.

The Pixel Detector The Pixel detector consists of silicon-based semiconductor pixels, located at three concentric layers close to the beam pipe. It provides the highest spatial precision measurement of the track. The typical pixel size is 50 400 µm2 resulting in around 80 million read- × out channels. A track ideally leaves one hit in each of the three layers, see Fig. 2.2. A HIP would by its extensive ionisation saturate the pixel detector and no hits would be recorded.

The Semiconductor Tracker The SCT contains four tiled double layers of silicon microstrips in the barrel and eight double layers in the end- cap. A particle traversing the SCT will leave up to 8 hits, each with an accuracy of 17 µm in R φ and 580 µm in z (barrel) or R (end-cap). − 34 Chapter 2. Experimental Overview

In contrast to the TRT, see below, the SCT does not record any information on the energy deposition which makes the TRT a more useful discriminator for HIPs.

The Transition Radiation Tracker The TRT includes the TRT barrel at 0 < η < 1.06 and end-caps at 0.77 < η < 2.15. The TRT is made | | | | out of 4 mm polyamide straw drift tubes filled with a gas mixture of 70% Xe, 27% CO2 and 3% O2, and has 350 000 read-out channels. The anode is mainly made out of tungsten covered with a thin gold film. The spatial resolution of the TRT is much lower than for the other tracker detectors, 130 µm. No positional measurements can be obtained in the straw direction, which lies along the z-axis in the barrel and along the radial direction in the end-caps. However, the number of measurements (the number of TRT straws traversed) per track is large, typically around 35. A particle is required to deposit at least 300 eV in a traversed straw, resulting in a low threshold TRT (LT TRT) hit. A deposition of 6 keV results in an additional high threshold TRT (HT TRT) hit. Minimum ionising particles deposit 2 keV. ∼ As can be anticipated from its name, the TRT was designed to identify relativistic particles by transition radiation. Layers of radiator material, where traversing relativistic particles emit transition radiation, are interleaved with the straws. The extra energy deposition from the transition radiation photons in addition to the usual ionisation, result in HT hits, whereas minimum ionising particles only give rise to LT hits. The high ionisation energy depositions from HIPs result in a large fraction of HT hits. The combined energy deposition of multiple low- energy electrons, δ-rays (see Sec. 4.3), will result in additional HT hits. A δ-ray with a typical 3 MeV kinetic energy is bent in the magnetic field and has a radius of 5 mm. This gives rise to a 1-cm-wide region of HT TRT ∼ hits around the HIP path, not present for electrons. The characteristic signature of a HIP in the TRT is used as a discriminating variable in the analysis presented in Chap.5. A validation of the TRT response to HIPs has been performed.

Calorimetry The calorimeter system of ATLAS consists of five subsystems as shown in Fig. 2.3, each based on different technologies to detect the kinetic energy of incoming particles by letting them shower, see Sec. 2.3. The electromagnetic calorimeter measures the energy of electrons and photons 2.3. The ATLAS Detector 35 and also contribute to measuring hadrons, while the hadronic calorimeter is constructed primarily to detect hadrons, which travel further and give rise to different showering processes. The total energy of an object, such as a particle, is then formed using information from both detector systems. The combined calorimeter system covers η < 4.9 and 1.4 < r < 4.25. | | More information can be found in Ref. [87, 99, 100, 101].

Figure 2.3: A cut-away view of the ATLAS calorimeter system. The ﬁgure is from Ref. [87]

The Electromagnetic Calorimeter The ElectroMagnetic Calorimeter (EM Calo) is a Liquid Argon (LAr) calorimeter. It consists of an absorber material, lead plates structured in an accordion shape, and an active material, liquid argon, ﬁlling the gaps between the absorbers, see Fig. 2.4. Two copper read out electrodes are placed in the middle of the gap over which a voltage of 2000 V is applied. Electrons from argon atoms which are liberated by the ionisation of a traversing particle typically drift the 2.1 mm gap in 450 ns. Electrons and photons shower in the absorber material. The pair- produced electrons and positrons ionise the argon and from this the energy 36 Chapter 2. Experimental Overview

Cells in Layer 3 ∆ϕ×∆η = 0.0245×0.05

Trigger Tower ∆η = 0.1 2X0

η =0 16X0 470 mm

Trigger Tower ∆ϕ = 0.0982

4.3X0

1.7X0 1500 mm ∆ϕ=0.0245 x 36.8mmx 4 =147.3mm4 Square cells in L ayer 2

∆ϕ = 0.0245 37.5mm/8 = 4.69 mmm ∆η = 0.025 ∆η = 0.0031 ϕ Strip cellsin Layer 1 Cells in PS ∆η×∆ϕ = 0.025×0.1

Figure 2.4: A wedge of the EM Calo barrel, showing the accordion structure of the absorber material and readout electronics as well as the layout and granularity of the diﬀerent layers. The ﬁgure is from Ref. [99].

deposition of the particle can be inferred. HIPs do not shower in this way1 and are detected by ionising the argon directly, see Sec. 4.2. The energy deposition is therefore much more concentrated than for an electron or photon. This is one of the two characteristic signatures of a HIP in the ATLAS detector, the other one being the large ionisation in the TRT, discussed above. The EM calorimeter consists of two barrels extending over η < 1.475 | | and two end-caps covering 1.375 < η < 3.2. There are three layers, | | EM1, EM2, EM3, of diﬀerent cell granularity plus a so called presampler covering η < 1.8, installed to estimate the energy losses in the structure | | material before the calorimeter, see Fig. 2.4. EM1 has a very ﬁne granu-

1However, for low mass HIPs, the high production of δ-electrons may induce a shower, see Sec. 4.2. 2.3. The ATLAS Detector 37 larity2 in η: the cells are 0.025/8 0.1 in ∆η ∆φ, while EM2 has a higher × × resolution in φ: 0.025 0.025 in ∆η ∆φ. EM3 has the same granularity × × as EM2 in η but is more coarse in φ with a cell granularity of 0.025 0.05 × in ∆η ∆φ. The resolution of the electromagnetic calorimeters is for × showering particles approximately: σ 10% p 0.7% (2.3) E ∼ E[GeV ] ⊕ where σ is the resolution of the energy. This means the resolution increases with energy. However, this is not true for the Missing transverse energy (see Sec. 2.3), as is discussed in Sec. 3.3.

The Hadronic Calorimeter The hadronic calorimeter system is composed of the Tile central barrel covering η < 1.0, Tile extended barrel at | | 0.8 < η < 1.7, LAr hadronic end-caps covering 1.5 < η < 3.2 and the | | | | LAr Forward CALorimeter (FCAL) at 3.1 < η < 4.9. In the Tile barrel, | | the active material is a plastic scintillator and the absorber material is iron. The resolution of the Tile barrel calorimeter cells is (0.1 0.2) 0.1 − × in ∆η ∆φ, and the energy resolution can approximately be expressed × as: ! σ 50% = p +3% (2.4) E E[GeV ] ⊕ where σ is the standard deviation of the energy.

The Muon Spectrometer The muon system is, together with the ID and the calorimeters, used to reconstruct the muon tracks. The muon system occupies the largest and outermost part of the detector, since the high momentum muons will travel through the other detectors without much interaction. The muon system covers η < 2.7 and is divided into precision measurement | | chambers and trigger chambers, as well as barrel and end-cap regions. The barrel chambers are interleaved with the toroidal magnets while the end-cap chambers are placed either behind or in front of the toroidal magnet. The resolution in the bending plane is 60-70 µm. More details can be found in Refs. [87, 102].

2The numbers given here are for the barrels, and for the η < 1.40 range. For | | 1.40 < η < 1.475 and in the end caps, the granularities are somewhat coarser, up to | | 0.1 0.1 in ∆η ∆φ. × × 38 Chapter 2. Experimental Overview

The Cathode Strip Chambers The Cathode Strip Chambers (CSC) are multi-wire proportional chambers are located in the end-cap region, 2 < η < 2.7. They are used in the innermost tracking layer because of | | their resistance to high rate radiation and their good time resolution.

The Monitored Drift Tubes The Monitored Drift Tubes (MDT) are cylindrically shaped gas-filled, pressurised aluminium tubes with a central anode tungsten-rhenium wire. Particles passing the detector ionize the gas particles and electrons drift towards the anode, giving the signal. The MDT covers 0 < η < 2.7. | | The Magnet Systems There are two magnet systems in the ATLAS detector. The innermost, the Solenoid, is a superconducting NbTi wire coil located between the ID and the calorimeters. It provides the ID with a 2 T field in the longitudinal direction that deflects charged particles in the transverse plane. The other magnet system, the Toroid, provides the muon system with a magnetic field in the φ direction [87].

Object Reconstruction, Data Acquisition and Processing The design bunch crossing frequency is 40 MHz, which corresponds to one crossing every 25 ns, is also the read out frequency. Up until and including 2012, the LHC has been run with 50 ns bunch spacing, giving 20 MHz in crossing rate [103]. The Data Acquisition System (DAQ) is responsible for the buffer- ing and transferring of data from the detector Read Out System (ROS) to permanent storage. The trigger system, which will be described in Sec. 2.3, makes a first selection of interesting events which will be stored and further processed. The trigger system is divided into three levels, Level 1 (L1), Level 2 (L2) and the Event Filter (EF). The DAQ is pipelining the data awaiting the trigger decision. The events selected by the trigger then proceed to the offline reconstruction processing, where the full detector information from the event along with calibration constants is fed into various algorithms to reconstruct the physics processes of the event. This is for example the energy, the particles and their properties as well as the vertices in the event. The reconstruction of energy sums, primary vertices, electrons/photons and hadrons will be discussed below. 2.3. The ATLAS Detector 39

At each LHC running period during which collisions take place, a so called trigger menu speciﬁes the set of triggers used at that time. The triggers are chosen taking into account the requests of the analysis groups but also considering the limit on the total trigger rate. The total trigger rate is the rate of events that are selected by any of the triggers in the menu, and is thus the rate of events that needs to be processed and saved permanently. The trigger signatures relevant to this thesis is Electron/Photon triggers, also referred to as Egamma triggers and MET triggers. The other main groups of triggers are muon triggers, jet triggers, tau triggers and B-jet triggers. Each of the triggers have their own instrumental implementation and software. Both the Egamma and the MET triggers are calorimeter triggers and will be discussed in Sec. 2.3.

Energy Sums

The energy sums, defined below, are computed differently at L1, (see Sec. 2.3) compared to EF (see Sec. 2.3) and in the offline reconstruction. At L1 the energy sums are computed using the energy deposition in so called jet elements which are collections of calorimeter cells. At EF and in the offline reconstruction, the full granularity cells are used, but only the energy of the reconstructed objects are included in the sums, where calibrations of the energy deposition for different objects have been carried out. Given below are the definitions of the different energy sums used in ATLAS. The transverse momentum and energy are explained in Sec. 2.3.

Ex, Ey: using the x, y and z coordinates of each in jet element (cell) in the detector, a vector, ~e, with ~e = the total (reconstructed) energy | | P deposition of that jet element (cell), is deﬁned. Then, Ex = i ex,i, P Ey = i ey,i, where ex,i and ey,i, are the x and y components of ~ei for a jet element (cell) i, and the sum goes over all jet elements (cells) of the detector (associated to a reconstructed object).

ET and MET: for an event, E~T = (Ex,Ey), and −−−→MET = E~T . MET − stands for missing ET and corresponds to the imbalance in transverse energy (momentum). If used without any reference to an object, ET most often refers to the magnitude of this vector, ET = q 2 2 Ex + Ey and MET then has the same value. For an object, ET is deﬁned as ET = E sin(θ). · 40 Chapter 2. Experimental Overview

sumET : using the deﬁnitions of ex,i and ey,i from above, sumET = P p 2 2 i (ex,i + ey,i ), where the sum goes over all jet elements (cells) of the detector (associated to a reconstructed object).

sumE: let ei be the total (reconstructed) energy deposition in a jet P element (cell) i. Then sumE = i ei, where the sum goes over all jet elements (cells) of the detector (associated to a reconstructed object).

Primary Vertex A vertex ﬁnding algorithm is applied to all the tracks of the event to reconstruct the so called Primary Vertices (PVs). A primary vertex corresponds to a primary interaction, that is between any of the components of the colliding protons.3 At high luminosity, there are many primary interactions in each event, this is referred to as pile-up. The number of PV’s depends on the luminosity conditions. For example, for the data periods used for this thesis, up to around 35 PV’s could be present per event.

Hadron Signatures Hadronic Jets In high energy collisions energetic quark-antiquark pairs are often produced and emitted in diﬀerent directions. A collection of new pairs of quarks forming hadrons will be produced through several steps of hadronisation and each quark will give rise to a so called hadronic jet in the direction of the original parton. Jets are characteristic of many particle collision events in ATLAS and are important signatures of many interesting particle interactions. The jets contain information about the original parton, but the hadronisation process is complicated to reconstruct and the algorithms devoted to this are required to be sophisticated.

Hadronic Showers A hadron entering the ATLAS hadronic calorimeter will “shower”, which means that it will interact strongly with the detector material and produce new particles through hadronisation. The newly produced hadrons will continue this interaction and more hadrons will be produced. The energy deposition of all the particles in the shower are detected to reconstruct the energy of the incoming hadron.

3A secondary interaction is a decay or interaction of any of the particles produced in a primary interaction. 2.3. The ATLAS Detector 41

Electron and Photon Signatures

Electromagnetic showering is a process by which an incoming electron or photon interact with the detector material by Bremsstrahlung, or electron positron pair production, respectively. The produced photon, or electron-positron pair, will then continue in the same manner, producing a so called electromagnetic shower. The shower continues until the energy threshold for Bremsstrahlung is reached and ionization losses become more important. From the shape of the shower the kinetic energy of the incoming particle can be inferred. In an electromagnetic calorimeter, the interactions occur in an absorber material and the magnitude of the shower is measured for example by the charge created by ionisation in a so called active material. In ATLAS, an electron candidate is constructed of a collection of adjacent cells in the electromagnetic calorimeter, a so called cluster4, and a matching track in the ID. A photon does not leave any track in the ID. An electromagnetic calorimeter cluster with an ID track vetoed is thus used to construct a photon candidate.

The Trigger System Introduction - The Three Level Trigger System

In order to reduce the amount of data permanently stored and processed, a dedicated system for online (run-time) selection of interesting events from the huge amount of non-interesting events is used. This is the trigger system. More detailed information on the ATLAS trigger system can be found in Refs. [87, 104, 105, 106]. The trigger system loosely classifies the events in terms of different physics scenarios or including specific objets such as electrons or muons, that could be of interest. These are referred to as trigger signatures, or just triggers. Each of the different triggers have their own independent criteria for an event to be categorized as such or not. If an event passes any of the triggers employed at that time, it will be saved to permanent storage. The events will be tagged according to which trigger(s) they passed and saved into corresponding event collections referred to as streams. An example is the so called Egamma stream including events which passed any of the electron/photon triggers.

4The construction of clusters in ATLAS is sophisticated and there are several different cluster algorithms at use. 42 Chapter 2. Experimental Overview

Figure 2.5: Overview over the trigger system data ﬂow. The ﬁgure is from Ref. [104].

The trigger system consists of three levels of selection and semi-separate systems, L1, L2 and EF. L1 reduces the event rate to 75 kHz. The L1 ∼ trigger system both makes the initial selection, as well as providing L2 with information for its more refined selection [104]. L2 reduces the event rate to 1 kHz. The EF performs the last selection of events using the ∼ offline reconstruction algorithms5 and the full event data, reducing the event rate to 400 Hz. ∼ The data flow of this process and the units responsible for each step are indicated in Fig. 2.5. Reduced granularity information is read out through trigger-specific on-detector electronics and transferred to L1 purpose-built hardware processors, which use this information to make the trigger decision, the so called L1 accept or L1 reject. The time it takes for L1 to deliver the decision to the detector front-end electronics is called the L1 latency and is < 2.5 µs.

5The essential difference between the EF level objects and the ones resulting after the offline reconstruction is that better tuned calibration constants and information on dead channels is used in the offline reconstruction. 2.3. The ATLAS Detector 43

The raw data from all the subdetectors are during the L1 latency stored in pipeline memories, see Fig. 2.5. At L1 accept, this data is transmitted to the Read Out Drivers (RODs), and further to the Read Out Buﬀers (ROBs). The RODs are interfaces between the data format of the read out system and the DAQ, to which the ROBs belong. Awaiting the decision of the L2 trigger, the data is next stored in the ROBs, all accessible to the L2 trigger system. Through a separate path, Region of Interests (RoIs), are transmitted from the L1 to the L2 system. RoI refers to a region in the calorimeter or muon system where the criteria of a L1 trigger have been met. Using this information, only a fraction of the data needs to be accessed from the ROBs in order to make the L2 decision. The information can if required be full-granularity, still the geometrical selection reduces the information used at L2 to a few percent of the full event data, making it possible to keep the L2 latency within 10 ms. Upon the L2 accept the data is transmitted to the Event builder system, which is where all the data from the event are collected from all the ROBs, and saved in a single memory. The EF trigger subsequently processes the event to make the ﬁnal trigger decision [104].

The Level 1 Trigger System Input Fig. 2.6 shows the L1 trigger information flow on the large scale. The two input systems are the calorimeters and the muon system. The format of the calorimeter information is analog signals from (reduced granularity) trigger towers. A trigger tower is a collection of calorimeter cells and typically covers an area of ∆η ∆φ = 0.1 0.1, × × but varies for different calorimeter sections, see Fig. 2.8. This information is processed by the calorimeter triggers, that is electron/photon, jet, tau lepton, MET and sumET triggers. The muon system, providing the muon trigger with information, has trigger-specific subdetectors referred to as Trigger chambers: the Resis- tive Plate Chambers (RPC) in the muon barrel and Thin Gap Chambers (TGCs) in the end-caps. Both systems detect the muon traversing three layers of chambers at different pseudorapidity, making use of the measured curvature of the muon path to estimate the pT .

Processing Calculations on the input data are carried out by calorimeter trigger system and the muon trigger system and multipicities of trigger thresholds passed are transmitted to the Central Trigger Processor 44 Chapter 2. Experimental Overview

Calorimeters Muon detectors

L1 trigger

Calorimeter triggers Muon trigger EM Emiss Jet T µ ET

Central trigger processor

Timing, trigger and Regions- control distribution of-Interest

Detector front-ends L2 trigger DAQ

Figure 2.6: Overview over the L1 trigger system data ﬂow. The ﬁgure is from Ref. [87]. 2.3. The ATLAS Detector 45

(CTP). Combining all the multiplicities according to the definitions of the triggers used at that time and comparing to the criteria, the L1 trigger decision is taken. If any of these triggers are fired (passed), a L1 accept is given. Inherent to the trigger system, is the difficulty to combine the trigger criteria and the different triggers in such a way that the signal efficiency is high at the same time as the overall accept rate is kept below the limit of the data processing and storage infrastructure. To be able to use more inclusive trigger criteria without exceeding the rate limit, so called prescaling, is sometimes carried out at the CTP level. This means that for some high-rate triggers, L1 will only deliver an accept in a certain fraction of the times this trigger has been passed technically. Another feature of the CTP is dead time control. Dead time can for example be imposed if overflow is likely in the front-ends or if L2 is to saturate. The time constraint on the CTP has been met by implementing the CTP as custom-built, pre-programmed hardware, such that no software is needed. The whole L1 is a system of synchronous processors timed by the LHC machine clock, a centralized clock used in all LHC experiments, running at 40 MHz. At every clock tick, one L1 decision is made.

Output As already discussed above the L1 accept and RoIs are sent to L2. The trigger decision is however also transmitted to the subdetector front-ends where the data is stored awaiting L1 accept. Upon reception of an accept, the data is transferred from here to the readout system.

The Level 1 Calorimeter Trigger On-detector The reduced granularity trigger towers are are built on- detector, in the Trigger Tower Boards (TBB), where analog signals are summed for each cell in the tower. The EM Calo energy is converted from total E to ET in two steps (see Sec. 3.4), where the ﬁrst approximate adjustment is carried out here, and the ﬁnal conversion is performed at the Receiver. The sums of each tower are then sent in 7200 individual ∼ cables to the Preprocessor via the Receiver.

The Receiver Data from the diﬀerent parts of the calorimeter arrive to the Receiver, see Fig. 2.7, grouped according to the layout of the calorimeter. At the Receiver, a remapping is performed whereby the electromagnetic and hadronic part of the trigger towers are asssociated with each 46 Chapter 2. Experimental Overview

LAr Tile/LAr (EM) Calorimeters (hadronic) On detector Analogue Sum ~7000 analogue links Twisted pairs, <70 m In USA15 Receiver

Pre-processor PPM's 10-bit FADC Bunch-crossing ident. To ROD's (for DAQ) Look-up table 2x2 sum BC-mux 9-bit jet elements 8-bit trigger towers

Serial links (400 Mbit/s)

JEM's CPM's Jet/energy processor Cluster processor To (e / and h EM+hadronic 2x2 sums ROD's To ROD's E sum Jet-finding (for Cluster-finding (for DAQ) T DAQ) Ex, Ey Local maximum Local maximum

miss ET,ET Counting CMM's Counting E RoI's T Jets e / h sums RoI's To ROD's (for L2) L1 muon trigger L1 central trigger processor

Figure 2.7: Block diagram of the L1 calorimeter trigger architecture. Ana- log data from the calorimeters are digitised and associated with the correct bunch-crossing in the Preprocessor and then sent to two algorithmic processors, the Jet/energy-sum processor and the Cluster processor. The resulting hit counts and energy sums are sent to the Central trigger processor. The ﬁgure is from Ref. [87]. 2.3. The ATLAS Detector 47

(a) EM Calo

(b) TileCal

Figure 2.8: Coverage and resolution of the trigger towers in (a) the electromagnetic and (b) hadronic calorimeters. The φ granularity is shown in the vertical direction, where for example in (a), the whole barrel has a trigger tower granularity of ∆φ = 0.1 as well as the barrel layers 1 and 2 in (b). The granularity in η is shown on the horizontal axis. The ﬁgures are from Ref. [104].

other, but still kept seperate. Conversion from E to ET is then carried out, before transmitting the information to the Preprocessor.

The Preprocessor The outputs of the Receiver are analog differential signals delivered to the Preprocessor in twisted pair cables. 10-bit ADCs in the Preprocessor digitize these analog signals. On the digitized signals Bunch Crossing Identification (BCID) is then carried out. Conversion from ADC signals to energy are then performed using Look Up Tables (LUT), which are static dictionaries, and results in 8 bits ET with a Least Significant Bit (LSB) of 1 GeV. 2000 parallel cables send this information with 2000 Gbits/s, to the close-by Cluster processor and Jet/Energy Module, see below. The signals are offset by a value, the pedestal, by construction to ensure positive signals when the digitisation 48 Chapter 2. Experimental Overview

Σ Σ

Σ Hadronic calorimeter

Electromagnetic calorimeter Trigger towers (∆η × ∆φ = 0.1 × 0.1) Electromagnetic Σ Vertical sums isolation ring

Σ Horizontal sums Hadronic inner core Local maximum/ and isolation ring Region-of-interest

Figure 2.9: Electron/photon and τ lepton trigger algorithm. The ﬁgure is from Ref. [87]. is performed. The pedestal is then subtracted after the digitisation is done. The LSB of 1 GeV imposes an implicit noise cut, meaning that up to 1 GeV is removed from all trigger towers. Trigger level noise cuts are discussed in some more detail in Sec. 3.3.

The Cluster Processor The Cluster processor searches for high pT electrons, photons and tau leptons by reconstructing clusters, collections of high energy trigger towers, see Fig. 2.9. For all 4 4 trigger tower col- × lections, referred to as windows, the four possible two-tower EM Calo energy sums indicated as “vertical” and “horizontal” of the 2 2 core × as indicated in Fig. 2.9 are evaluated and compared to programmable thresholds. These 2 2 inner cores constitute the electron/photon/tau × RoIs. To avoid overlap between clusters, the core is required to be a local maximum. For photons/electrons, a (programmable) isolation veto can be imposed, either on the EM Calo energy deposition in the 12 towers surrounding the core, or on the energy deposition in the hadronic calorimeter of the 2 2 inner core. These two diﬀerent isolation regions are indicated × in Fig. 2.9 and referred to as the electromagnetic isolation ring and the 2.3. The ATLAS Detector 49

Window 0.4 x 0.4 Window 0.6 x 0.6 Window 0.8 x 0.8

Figure 2.10: A schematic view over the jet trigger algorithm. The algorithm is based on 0.2 0.2 in ∆φ ∆η jet elements, shown as squares × × in the figure, and aims at finding a jet RoI, shown as shaded areas in the figure. In the 0.6 0.6 window there are four possible RoIs. In the × 0.8 0.8 case the RoI has to be in the centre position, in order to avoid × two RoIs in the same window. The figure is from Ref. [87].

Hadronic inner Core (HadCore), respectively. A study of triggers using isolation vetoes are presented in Sec. 3.2. For tau leptons, the four possible two-tower sums in the hadronic core are instead added to the possible electromagnetic two-tower sums, and the threshold is imposed on the combined sum. Two diﬀerent isolation thresholds for the electromagnetic and hadronic isolation rings respectively are then imposed.

The Jet/Energy-sum Processor The base of the jet algorithm is the jet element, a collection of 2 2 trigger towers (including both electro- × magnetic and hadronic calorimeter cells). Any of the three types of so called windows, corresponding to three diﬀerent algorithms, are nominally formed around the jet elements, see Fig. 2.10. The ET of each window is compared to a threshold and a trigger jet candidate is generated if the threshold is passed and the RoI is a local ET maximum. In the Jet/Energy Modules (JEMs), which are the physical units of the Jet/Energy-sum processor, Ex, Ey and ET (see Sec. 2.3) summations over all the jet elements are then carried out.

The Common Merger Module The Cluster processor and the Jet/Energy- sum processor are divided into several sub processors. The Common Merger Modules (CMMs) are responsible for combining the results from all these sub processors. The multiplicities of clusters/jet candidates passing the diﬀerent energy thresholds are added and all Ex, Ey and ET sums are combined into the total MET and the sumET for the event. The 50 Chapter 2. Experimental Overview sums are compared to eight and four programmable thresholds, respectively. These results, along with 8-bit Ex and Ey are sent to the CTP.

2.4 The SQUID Magnetometer and a Monopole Signature

This section gives a brief introduction to a Superconducting QUantum Interference Device (SQUID) [107, 108]. A SQUID is a magnetometer which, for the purposes of the research in this thesis, measures the current induced by a magnetic field as a magnetic sample passes through a superconducting coil (sense coil). The current induced by a magnetic dipole field will increase until it reaches a certain plateau when the sample producing the field is at the centre of the sense coil and and then returns to zero when it has passed the coil. For monopoles, the current will per- sist at the plateau even after the sample has passed the coils. The value of the plateau will be proportional to the magnetic field flux associated with the monopole. The above can be understood by considering the generalized Faraday’s law (see Eq. 1.35): Z d Z Z ε = E~ d` = B~ dS~ µ0 j~M dS~ (2.5) loop · −dt S · − S · where ε is the electromotive force induced in the superconducting coil by the magnetic field, B~ , from a magnetic sample passing through the coil and E~ is the induced electric field in the loop. The quantity jM is the magnetic current, and S is a surface of arbitrary shape bounded by the loop. Choosing S to be infinitely large, (e.g. like a large expanding bal- loon) implies that the jM term need not be considered since no magnetic charge crosses the surface. A current i is induced in the superconducting di dφint loop inducing an electromotive force εint = L dt = dt and a flux, φint, d R − opposing the magnetic sample, φext = B~ dS~ . The parameter L is dt S · here the inductance of the loop. No flux is allowed in a superconductor and the φint must perfectly cancel the flux from the magnetic sample:

di dφext L = ( ) (2.6) dt − − dt Li = φext (2.7) Inducing a net flux through the surface S, dipoles will be detectable as a current in the coils when they pass through them. At large distances from 2.4. The SQUID Magnetometer and a Monopole Signature 51 the coils the net flux from the dipole is however zero, and as the dipole moves away from the coils the current recedes and eventually vanishes. For a monopole, however, the net flux through the surface will remain non-zero even after having passed the loop, and there will be a detectable persistent current in the loops. Gauss’ law for monopoles, Eq. 1.34 then gives the monopole charge:

φext µ g i = = 0 (2.8) L L The SQUID is designed as a sensitive magnetometer to measure small changes of a magnetic ﬁeld. It can measure ﬁeld changes as low 5aT i.e. 5 10−18 T. × 52 Chapter 3

ATLAS Level1 Trigger Studies

In this chapter my work concerning the ATLAS Level1 trigger system is presented, parts of which are published in Paper I. The beginning of the chapter introduces some concepts relevant to the trigger studies I have made. Following this, the three diﬀerent research projects I was involved in are presented in Sec. 3.2, Sec. 3.3 and Sec. 3.4. In each of these sections the research results will be preceded by an introduction where a theoretical background or the experimental set-up will be explained.

3.1 Trigger Eﬃciency and Bootstrapping

A trigger chain is a combination of a specific L1, L2 and EF trigger that are used together. The combined trigger efficiency of this chain is one of the components in the total selection efficiency for physics analyses employing this trigger chain, and is therefore a very important quantity to measure. When the number of events measured , the efficiency, , is de- → ∞ scribed theoretically as

theo = P (T c) (3.1) | where P (T c) stands for the probability of triggering on an event, using | the requirements of a trigger, T , given that the event belongs to a set of interesting events denoted as c, short for the conditions imposed to select these events. A trigger efficiency is characterised by a low efficiency for low energy values, a so called turn-on around the energy threshold of the trigger criterium where the trigger starts being efficient, and a plateau of high

53 54 Chapter 3. ATLAS Level1 Trigger Studies efficiency reached after the turn-on. Examples of trigger efficiency curves can be found in Sec. 3.2. The shape of the turn-on region describes the energy resolution of the trigger. Theoretically, the trigger is simply a discriminator, which gives a pass or fail decision. The efficiency would therefore be a step function, S(x):

0 if x < X S(x) = threshold (3.2) 1 if x Xthreshold ≥ where Xthreshold is the trigger threshold value, and x is a theoretical prop- erty of the particle, such as the energy. Adding the eﬀect of the gaussian distributed calorimeter trigger energy resolution, σ, yields a step func- 2 − t tion convoluted by a gaussian, e σ2 dt, referred to as the Error function, erf(x).

Z ∞ 2 2 − t erf(x) = S(x t) e σ2 dt (3.3) σ√π −∞ − · Z x−Xthreshold 2 2 − t = e σ2 dt (3.4) σ√π −∞ The parameter t represents the measured energy assumed to be centered around the true value x. Additional smearing arises for trigger efficiencies as functions of offline reconstructed observables, since there are large differences in how the quantities are calculated at trigger level and offline. For example, at L1, the energy sums are digitized after analog summing of the trigger tower energies, while in the offline algorithms the digitisation is performed at cell level before summing. In Sec. 3.3, a double error function, a linear superposition of two error functions, is used to account for this. The free parameters are the two different standard deviations and the effective thresholds of the two distributions respectively. Measuring the trigger efficiency in reality will introduce a bias with respect to Eq. 3.1. Ideally the trigger efficiency would be measured on random triggered events, but this can only be done for very low energy threshold triggers1 such as MET > 20 GeV and in most practical cases another trigger, S, has to be used to obtain statistical precision:

measured = P (T S, c) (3.5) | 1Only for triggers with low energy thresholds, random triggered event will provide enough statistical precision in the turn-on region, as most events in ATLAS are of low energy. 3.2. L1 Single Electron/Photon Triggers 55 where measured is the measured trigger eﬃciency of the trigger T . To obtain P (T c) from P (T S, c), both P (S c) and P (S T, c) have to be mea- | | | | sured. Using Bayes’ theorem: P (S c) P (T c) = P (T S, c) | for P (S T, c) > 0 (3.6) | | · P (S T, c) | | Usually P (S c) can be measured on randomly triggered events, but P (S T, c) | | is less straightforward. If, for example, the trigger S is an electron trigger and T is a MET trigger, there might not be enough electrons in the events triggered by T alone. However, the ratio P (S c)/P (S T, c) can often be | | estimated from simulations or argued theoretically. For MET triggers, a method called bootstrapping is often applicable. By requiring S to be a trigger with looser requirements than T , fulﬁlling:

P (S T, c) = 1 (3.7) | for all energies, the P (S T, c) does not have to be measured. If Eq. 3.7 | holds, then

P (S c) = 0 = P (T c) = 0 (3.8) | ⇒ | which is important since no information can be obtained from the P (S c) = | 0 region. If the trigger S is chosen such that the diﬀerence in energy thresholds between S and T ensure:

Introduction The L1 single electron/photon triggers are among the most inclusive and widely-used triggers on ATLAS and a high signal eﬃciency is therefore very important. As no distinction between electrons and photons are made at L1, both HLT electron and HLT photon triggers makes use of 56 Chapter 3. ATLAS Level1 Trigger Studies

L1 single electron/photon triggers. The study presented in this section concerns the electron trigger efficiency of the L1 single electron/photon triggers. The e22 medium1 trigger chain [109] is one of the most used trigger chains based on L1 single electron/photon triggers. The e stands for one electron and 22 for the ET threshold imposed on this electron. The medium12 represents the level of requirements in the electron identification algorithm at EF level. The selection variables used at EF are similar to those used in the offline reconstruction, which are related to the shower shape in the EM Calo. These cuts are optimised for rejection of the backgrounds for electron and photon: heavy flavour3, neutral and charged mesons, typically the π0 decaying into two photons. More details can be found in Refs. [109, 111]. The e22 medium1 trigger chain was at the beginning of the summer of 2011 based on L1 EM16. This trigger basically requires a EM Calo trigger cluster, see Sec. 2.3, with ET > 16 GeV. In general, L1 triggers requiring an EM Calo cluster are referred to as L1 EM triggers, and the same nomenclature is used for all L1 EM triggers. For example L1 EM17 and L1 EM18 require a cluster ET > 17 GeV and > 18 GeV, respectively. The instantaneous luminosity at the LHC restart in March 2011 reached 5 1032 cm−2s−1 and it was planned that it would steadily continue × to rise as the LHC was managing to increase the number of protons per bunch and focus the beam size at the interaction point [112]. In September the same year, peak instantaneous luminosities on the order of 3 1033 cm−2s−1 were expected, and also expected to continue increasing. × This was also accomplished, see Fig. 3.1. The problem of increasing trigger rates for the e22 medium1 trigger chain that would follow needed to be solved without compromising the signal efficiency considerably, as would have happened with the most straightforward solution, simply raising all thresholds. More subtle methods were required, and I was involved in two such attempts concerning the L1 electron/photon trigger used in this chain: pseudorapidity-dependent thresholds and hadronic leakage veto, as described in the following sections. The combination of the two ap-

2There are loose, medium and tight, where loose refers to the most inclusive requirements. More information can be found in Ref. [110]. 3Hadrons containing charm or bottom quarks, are referred to as being heavy ﬂavour objects. Some of these may decay to photons and leptons, but which are often close to a hadronic jet, which can be used for discriminating them from primary interaction photons/leptons. 3.2. L1 Single Electron/Photon Triggers 57 ] •1

s 10 •2 s = 7 TeV s = 7 TeV s = 8 TeV ATLAS cm

33 Online Luminosity 8

4 Peak Luminosity [10 2

0 Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Month in 2010 Month in 2011 Month in 2012

Figure 3.1: Peak instantaneous luminosities for 2010, 2011 and 2012. The ﬁgure is taken from Ref. [113]. proaches was later implemented and will brieﬂy be discussed at the end of this section.

Tag and Probe To evaluate the trigger efficiency, a so called tag and probe method was used in the studies concerning L1 single electron/photon triggers. The basic idea of the tag and probe method is to “tag” events that are known to include the object the trigger is to be tested for, by means of identifying another object in the event. This way the trigger used to select the events does not bias the measurement. Here, the process Z e+ + e− → is studied. Events in which this process takes place will include two high momentum electrons which could pass a L1 single/electron trigger, for example L1 EM16. By only requiring one electron to fire this trigger, where this electron is referred to as the “tag” electron, the trigger efficiency can then be evaluated for the other electron, the “probe” electron.4

Pseudorapidity Dependent Thresholds The electron trigger eﬃciency is dependent on pseudorapidity due to the geometrical layout of the detector. The study presented here concerned

4Since in this case, both the tag and probe are the same object, the case where both electrons pass the trigger has to be counted twice. This can be realised by identifying the four possible different configurations 00, 01, 10, 11 of pass and not pass for the two electrons, where only the last case will be measured as passed, and summing the probabilities. 58 Chapter 3. ATLAS Level1 Trigger Studies constructing new triggers taking this dependency into account. Differences in the trigger efficiency between different pseudorapidity regions are explained by the different amount and type of ID supporting material and services that an electron has to traverse before reaching the EM Calo. The electron will interact with the material and lose energy through Bremsstrahlung. A description of the material in the ID is shown in Fig. 3.2, where it is expressed in terms of units of radiation lengths. Fig. 3.2 shows the distribution in material of both “Services” and specific ID sub-detectors. “Services” here refers to the services and supporting structure in the envelope enclosing the ID, and the services internal to the sub-detectors are included in the specific sub-detector contributions. In the figure, the sudden increase in material at the ID transition region between barrel and end-cap starting at around η = 0.7 can be seen, as | | well as a second increase at around η = 1.3. This is cooling connections | | at the end of the TRT and SCT barrels, TRT electrical connections and other SCT and TRT services. Also visible in the figure are the ends of the TRT and SCT end-cap regions, at around 1.7 < η < 2.5. | |

] 3 0 ATLAS Services 2.5 Simulation TRT SCT Pixel 2 Beam•pipe Extra material

Radiation length [X 1.5

0.5

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 |η|

Figure 3.2: Stacked histograms showing the ID structure in terms of the radiation length. Services refers to up-holding structure magnets and other services, external to the sub-detectors. The ﬁgure is from [87].

Triggers where this pseudorapidity dependence of the efficiency is taken into account were constructed and the trigger rate and trigger efficiency were both being taken into consideration. The rate was to be 3.2. L1 Single Electron/Photon Triggers 59 reduced as much as possible without more than a few percent in efficiency loss. Fig. 3.3 shows electron trigger efficiencies for the three different L1 electron/photon triggers L1 EM16, L1 EM17 and L1 EM18. Data from the Egamma stream (see Sec. 2.3) period F - H1 (minus a couple of runs) were used.5 The efficiency disrtibutions of the various triggers only differ in the position of the turn-on. Comparing the different pseudorapidity regions to each other, the most crucial region is where the e22 medium1 has reached its plateau, but where the efficiency is still sensitive to small changes in the trigger criteria. In Fig. 3.4 the efficiency loss for different pseudorapidity regions are shown for 25 GeV < ET < 27 GeV and 27 GeV < ET < 30 GeV, separately. This is the region for which 25 GeV < ET < 30 GeV. Hardware restrictions in the L1 trigger cluster algorithm forced the pseudorapidity regions to be in steps of 0.4 in η. As is shown in Fig. 3.4, the difference in efficiency between the triggers is only of the order of 0.5% in the most central region, 0 < η < 0.4, for | | 25 GeV < ET < 27 GeV and even less for 27 GeV < ET < 30 GeV, for which this also holds in the 0.4 < η < 0.8, 2.0 < η < 2.4 and 2.4 < η | | | | | | regions. The difference is of the order of 1% in the 0.4 < η < 0.8 and | | 0.8 < η < 1.2 regions as well as in the regions for which η > 1.6 for | | | | 25 GeV < ET < 27 GeV. The same order of magnitude of the difference holds for the 27 GeV < ET < 30 GeV in the 0.8 < η < 1.2 and 1.8 < | | η < 2.0 regions. In the 1.2 < η < 1.6 region the difference in efficiency | | | | is between 3% and 7% for both ET regions, which is explained by it being the most material intense, see Fig. 3.2. The transition region between the EM Calo barrel and end-cap regions at around η = 1.375 also contributes | | to the efficiency drop in this region. Using the result in Figs. 3.3- 3.4, a set of new triggers were designed and evaluated with respect to trigger rate predictions for instantaneous luminosity 5 1033 cm−2s−1. As mentioned in Sec. 2.3, the L1 trigger × rate limit is 75 kHz. During 2011, 60 kHz was maintained, allowing for the possibility that the expected increase in instantaneous luminosity would not be perfectly matched with efficiency improvements of the triggers. The rate is nominally split between the trigger groups, such that electron/photon, muon and and tau/jet/MET triggers each are allowed 20 Hz. Given that the single electron/photon trigger being the most ∼ 5The LHC collisions and data taking are divided into periods of time where the run conditions are stable and similar. There were 12 periods during 2012 each divided into smaller sub periods. 60 Chapter 3. ATLAS Level1 Trigger Studies

(a) η < 0.4 (b) 0.4 < η < 0.8 | | | |

(e) 1.6 < η < 2.0 (f) 2.0 < η < 2.4 | | | | Figure 3.3: Trigger efficiencies for three L1 single electron/photon triggers of the different ET thresholds 16, 17 and 18 GeV with respect to offline electrons for different pseudorapidity ranges. 3.2. L1 Single Electron/Photon Triggers 61

(a) 25 GeV < ET < 27 GeV. (b) 27 GeV < ET < 30 GeV.

Figure 3.4: Trigger efficiency loss for three L1 single electron/photon triggers of the different ET thresholds 16, 17 and 18 GeV for different pseudorapidity regions for the offline 25 GeV < ET < 27 GeV (left), and 27 GeV < ET < 30 GeV (right). The efficiency is with respect to offline electrons.

“L1 EM16V 1” η < 0.8 0.8-1.2 1.2-1.6 1.6-2.0 2.0-2.4 ET,threshold [GeV] 18 17 16 17 18 “L1 EM16V 2” η < 1.2 1.2-1.6 > 1.6 ET,threshold [GeV] 18 16 18

Table 3.1: Two proposals of the implementation of a trigger L1 EM16V with pseudorapidity-dependent ET thresholds. 62 Chapter 3. ATLAS Level1 Trigger Studies

Rate predictions [kHz] L1 EM16 28.0 “L1 EM16V 1” 22.6 “L1 EM16V 2” 20.7

Table 3.2: Rate predictions for the two proposals for “L1 EM16V 1” presented in Tab. 3.1 and for L1 EM16 for an instantaneous luminosity of 5 1033 cm−2s−1. × important electron/photon trigger, it is allowed to take a large proportion of that rate. There are of course overlaps between the triggers. Two proposals of triggers were developed for which the signal eﬃciency losses in the region 25 GeV < ET < 30 GeV compared to L1 EM16 is only on the order of 1% and for which the predicted trigger rate for an instantaneous luminosity of 5 1033 cm−2s−1 was decreased with around 3 8 kHz × − compared to L1 EM16, giving rates that were satisfactory with respect to the overall electron/photon trigger rate. The triggers, “L1 EM16V 1” and “L1 EM16V 2”, are presented in Tab. 3.1 and the corresponding rates are given in Tab. 3.2. The V refers to variable thresholds.

HadCore Leakage Veto

Electrons and photons will ideally not deposit any energy in the hadronic calorimeter. A veto on the amount of energy deposited in the HadCore of a L1 EM cluster, see Sec. 2.3 and Fig. 2.9, can thus be imposed to improve the rejection efficiency against the hadronic background. To evaluate the efficiency loss for such an implementation, the L1 EM16 efficiency with three different isolation requirements imposed was investigated: HadCore energy 1, 2 or 3 GeV. The data used were from ≤ periods F - G5 of 2011 (minus a couple of runs). The efficiencies are presented in Fig. 3.5, evaluated with respect to offline medium1 electrons with ET > 25 GeV, since this is the ET region contributing most to high rate of the e22 medium1 trigger chain. The different triggers were called “L1 EM16H 1”, “L1 EM16H 2” and “L1 EM16H 3”, where H refers to hadronic leakage and 1,2 and 3 are the isolation requirements of 1, 2 and 3 GeV respectively. As expected from the fact that there is already a hadronic leakage cut applied offline relative to the electron pT , the efficiency loss is negligible. Some irregular efficiency drops can be seen for ET > 80 GeV. This is likely 3.2. L1 Single Electron/Photon Triggers 63

(a) (b)

Figure 3.5: Trigger efficiencies vs the offline ET ((a) and (b)), presu- dorapidity (c) and number of primary vertices (d) for “L1 EM16H 1”, “L1 EM16H 2” and “L1 EM16H 3”. Figure (b) is the same as figure (a) but the y-axis is zoomed in at the interesting region. an effect of the limited statistical precision of the data sample, since the momentum distribution of electrons in Z e+ + e− events is decreasing → exponentially. For higher energy electrons, the efficiency losses might be larger. For these events, the HadCore veto triggers can be used in combination with a higher threshold ( 60 GeV) trigger with no hadronic ∼ leakage veto applied, to obtain high efficiency. The efficiency as a function of pseudorapidity shows how the hadronic leakage affects different regions in the detector. The efficiency drops to at most 99.5% outside the transition regions at around η = 1.375 between the electromagnetic barrel and end-caps, where it drops to around 99%. To evaluate the in-time pile-up (several interactions in the same bunch- crossing, resulting in several high-energy primary vertices), the efficiency as a function of the offline reconstructed number of primary vertices in an 64 Chapter 3. ATLAS Level1 Trigger Studies

Rate predictions [kHz] L1 EM16 28.0 “L1 EM16H 1” 20.8 “L1 EM16H 2” 22.4 “L1 EM16H 3” 24.0

Table 3.3: Rate predictions for the three different HadCore leakage vetoes and for L1 EM16 for comparison, at an instantaneous luminosity of 5 × 1033 cm−2s−1.“EM16H x” refers to a HadCore energy of x GeV. ≤ event was studied. For the tightest isolation requirement, the HadCore energy 1 GeV, the efficiency is slightly in-time pile-up dependent. How- ≤ ever since the overall efficiency drop is so small, on the order of 0.2%, this effect is small enough not to affect the physics analyses considerably. The other isolation thresholds have efficiency drops on the order of 0.002%. Rate predictions for the different HadCore vetoes and the L1 EM16 trigger for an instantaneous luminosity of 5 1033 cm−2s−1 are presented × in Tab. 3.3. Compared to L1 EM16, the HadCore vetoes reduce the trigger rate with between 4 and 7.2 kHz. Considering both the insignificant efficiency loss of “EM16H 1” and the large predicted rate reduction, the conclusion of the study was that “EM16H 1” constituted the best choice of the investigated triggers.

Conclusions and Further Developments As part of a coherent program to make the calorimeter triggers more efficient in preparation for an expected increase in luminosity, two approaches were studied for single electron/photon triggers. The first study concerned an implementation of pseudorapidity-dependent energy thresholds and the second concerned a HadCore isolation veto. Proposals for new triggers were presented in both studies. The combination of the hadronic leakage veto and pseudorapidity- dependent thresholds, named L1 EM16VH [109], was implemented from period L 2011. The HadCore veto used was 1 GeV and the pseudorapidity- dependent ET thresholds as presented in Tab. 3.1 as EM16V 1. The measured trigger rates for different instantaneous luminosities for the trigger chain e22medium6 and the new one e22vh medium1, where L1 EM16 has been exchanged for L1 EM16VH, are shown in Fig. 3.6. As can be seen in

6An earlier version of e22medium1, comparable in terms of rate. 3.3. Performance of the MET Signiﬁcance Trigger 65

100 ATLAS Preliminary Rate [Hz] 80

40 e20_medium e22_medium 20 e22vh_medium1

0 0 5 10 15 20 25 30 35 40 Instantaneous luminosity [cm•2s•1] ×1032

Figure 3.6: Measured trigger rates for three different electron trigger chains. The trigger e22 medium, used together with L1 EM16, was from period L 2011 replaced by e22vh medium1 used together with L1 EM16VH. The graph is taken from Ref. [109]. this figure, the trigger rate of e22vh medium1 is significantly lower than for the e22medium.

3.3 Performance of the MET Signiﬁcance Trigger

Introduction

This section concerns the performance of the MET significance trigger, referred to as the XS trigger, which is a development of the MET trigger, introduced in Sec. 2.3. Along with the increasing instantaneous luminosities of 2011, pile-up was expected to increase, as discussed in Sec. 3.2. The pile-up can be represented by the Poisson parameter µ, defined as the average number of collisions per bunch crossing. When µ increases, the average energy deposition increases and the sumET and MET trigger rates increase more rapidly than linearly. The shape of the sumET distribution for different values of µ is shown in Fig. 3.7 and it is shown how the sumET distribution also broadens with increasing pile-up. The MET triggers will be affected due to the fact that the fake MET, described in the next section, scales with sumET . To avoid losing the lower energy thresholds important for higher energy trigger studies and for the sensitivity of many beyond SM searches which typically include a weakly only 66 Chapter 3. ATLAS Level1 Trigger Studies

10-1 ATLAS Preliminary µ = 4 s = 7 TeV µ = 6 10-2 µ = 8 µ = 10 10-3 µ = 12

Fraction of events µ = 14 µ = 16 10-4

10-5

10-6

0 100 200 300 400 500 600 700 800 900 1000

EF Y ET [GeV]

Figure 3.7: EF level sumET distributions for various values of the average interaction per bunch crossing, µ, for a random triggered collision data. The ﬁgure is from Ref. [1].

interacting particle the need for a more intelligent trigger was considerable. In preparation for a possible future implementation, the performance of the XS trigger was studied to make sure it was stable and well-understood. I studied the signal trigger efficiency using W e + ν and W µ + ν → → events. In the latter case trigger and offline XS related quantities were also studied and trigger efficiencies for collision data were also compared to simulated data. An implementation of the XS trigger in the trigger hardware and software was simulated. Before presenting the results, the reader will be introduced to the research motivating the XS trigger, the operational definitions and hardware simulation and, finally, calorimeter noise cuts affecting the distributions.

MET and Fake MET

The quantity MET (see Sec. 2.3) is an observable representing particles that do not interact with the detector. So called fake MET is defined as MET which does not originate from a non-detectable particle. The fake MET has two contributions: finite calorimeter resolution and a real imbalance in the transverse energy measurement. This imbalance can for example arise from hardware problems, mismeasured jets or cosmic rays. 3.3. Performance of the MET Significance Trigger 67

The contributions to fake MET vary between different types of processes. For low momentum transfer scatterings, which are the most common processes in events in ATLAS, fake MET arises from finite detector resolution only. This detector resolution can be modelled as is described in the next paragraph. These interactions make out the largest portion of events with low fake MET (of the order of 1 20 GeV). The largest contri- − bution to high fake MET is instead high momentum transfer interactions resulting in two high pT jets, which are also common in ATLAS events. For these interactions, mismeasurements of the total energy deposition of each jet, for example different fractions of EM conversions, gives rise to fake MET.

Modelling of sumET and Fake MET

As mentioned above, the dominant contribution to fake MET at low to moderate values is low momentum transfer scatterings which result in uniformly distributed energy in the calorimeter, and the finite calorimeter resolution gives rise to fake MET. An analytical model for the calorimeter detector resolution for these interactions has been developed and shows 7 that it is dependent on the sumET only. The fake MET can therefore for these interactions be parametrised as a function of sumET as will be described in this section. For random triggered events, the dominant contribution to the MET miss is fake MET. Fig. 3.8 shows Ex , the x component of the −−−→MET , for miss random triggered events for two different √sumET intervals. The Ex miss (Ey ) is gaussian distributed around zero and with a standard deviation linear in √sumET . This proportionality is independent of µ, provided the calorimeter cell calibration is constant. Since the fake MET component distributions for fixed sumET are gaussians, the fake MET for the same sumET is a Rayleigh distribution, R:

2 ! METfake METfake R(METfake; σ) = exp (3.11) σ2 − 2σ2

7The energy resolution of the total energy measurement of the calorimeter is to ﬁrst order √Nσ, where N is the total number of energy depositions (assumed to be ∼ of the same order of magnitude), and σ is the individual energy uncertainty of each measurement, also assumed of be the same for each energy measurement. Thus fake MET originating from the ﬁnite calorimeter resolution N sumET . ∼ ∼ 68 Chapter 3. ATLAS Level1 Trigger Studies

107 103 χ2 / ndf 63.52 / 22 ATLAS Preliminary χ2 / ndf 66.77 / 66 ATLAS Preliminary 6 ± ± 10 Constant 3.455e+04 7.204e+01 s = 7 TeV Constant 5.411 0.570 s = 7 TeV Mean 0.8186 ± 0.0070 Mean -0.0103 ± 1.3434 5 Sigma ± Σ ≤ 2 ± Σ ≤ 10 4.17 0.01 5 < ET 5.25 10 Sigma 16.71 1.76 17.5 < ET 17.75 Events/GeV Events/GeV 104

103 10

102

10 1

-1 -1 10-50 -40 -30 -20 -10 0 10 20 30 40 50 10-50 -40 -30 -20 -10 0 10 20 30 40 50

L1 Ex [GeV] L1 Ex [GeV]

(a) 5 < √sumET < 5.25 (b) 17.5 < √sumET < 17.75

miss Figure 3.8: L1 Ex distributions from randomly triggered collision data for two specific √sumET intervals, together with the gaussian fits. The figures are from Ref. [114]. where the parameter σ is the standard deviation of the component distributions and is parametrized as follows: p σ = a ( sumET b) (3.12) · − The parameters a and b are constants obtained from fits to data. The parameter σ is referred to the resolution.

The MET Significance Trigger The XS trigger was developed so as to improve the low to moderate fake MET rejection efficiency while maintaining high signal efficiency by considering the fake MET distribution as a function of sumET , as discussed in the previous section. The MET significance is defined as the MET in units of standard deviations of the fake MET distribution, using the specific sumET of the event. The MET significance is accordingly by construction robust with respect to background rejection even for increasing pile-up, keeping the rates down at increasing instantaneous luminosity [115].

Theoretical Deﬁnition

Using Eq. 3.11, the probability for the fake MET, METfake, to be larger than a measured MET value t can be obtained by integration: t2 P (METfake > t sumET ) = exp (3.13) | −2σ2 3.3. Performance of the MET Signiﬁcance Trigger 69

In effect, this expression gives the probability that the MET that is measured originates from resolution effects only. The statistical significance, Z, is now defined as the number of standard deviations corresponding to the probability 1 P for a gaussian distribution, G(x, σgauss) with the − same mean:

2 −1 −1 t Z = Φ [P (METfake t sumET )] = Φ [1 exp ] (3.14) ≤ | − −2σ2 Y 2 = Φ−1[1 exp − ] (3.15) − 2 where Φ−1 is the inverse of the cumulative of the gaussian distribution, giving x/σgauss. The quantity Y = t/σ asymptotically approaches Z, and the relation can be linearly approximated as Z = 1.07(Y 0.879). The − theoretical MET signiﬁcance, XStheo, is then deﬁned to be Y :

MET XStheo = Y = p (3.16) σ( sumET )

Operational Deﬁnition

Fits to randomly triggered events such as the ones shown in Fig. 3.8 give the constants a and b in Eq. 3.12. This allows for an up-to-date operational deﬁnition of the XS trigger. For the studies in this report, the operational L1 XS deﬁnition was:8

MET XSL1 = (3.17) 1.12 (√sumET 1.28) · − and the L2 has the same operational deﬁnitions since the same values of Ex and Ey are used. At EF level, the XS was deﬁned as:

MET XSEF = (3.18) 0.46 (√sumET 0.5) · −

Here the MET and the sumET are the measured values at L1 and EF, respectively.

8The values of a and b vary between runs and were changed once during 2011, as a compromise between accurate values and the eﬀort to minimise changes in the trigger settings. 70 Chapter 3. ATLAS Level1 Trigger Studies

Hardware Implementation Simulation L1 XS To emulate an implementation of the XS trigger in the trigger hardware and software, part of the current implementation had to be emulated as well, as only some of the intermediate steps of the calculations of the trigger system are saved to data. As discussed in Sec. 2.3, the Ex and Ey components of each jet element are summed at the JEMs, and the sums are then transmitted to the CMMs. The quadratic sum is here performed by LUTs to retrieve the MET value. To obtain precision at low values, four different LUTs for four different energy ranges are used. The values are then sent into the LUT in 8 bits, the first two giving the energy range it belongs to, and the resulting MET is on the same format. (The least significant bits exceeding 6 were dropped.) This was emulated in the code with bit masking. The MET significance was next calculated according to Eq. 3.17, with the following additions.

Automatic rejection if any of these are fulﬁlled: • √sumET > 63 GeV • √sumET < 3 GeV • MET < 11 GeV • Automatic acceptance if any of these are fulﬁlled: • Ex/Ex too large for the LUT • MET > 63 GeV • The automatic rejections/acceptances are due to hardware constraints at 1/2 L1, which use 6 bit words for expressing √sumET and MET (in GeV and GeV respectively). A very large √sumET (low MET) means a low XS value and automatic rejection is therefore imposed in this case. Auto- matic acceptance is instead imposed for very large MET. To avoid division by zero, the √sumET value must be above a minimum. Automatic acceptance overrides automatic rejection.

L2 XS The same values for Ex and Ey as for L1 are used at L2. The improvement in resolution comes from the calculation of MET which is calculated analytically. The XS values of L1 and L2 do still not differ significantly. The atomatic rejection and acceptance rules are the same as for L1, except for the one related to the LUT, which is not present at L2. 3.3. Performance of the MET Significance Trigger 71

EF XS The values of Ex and Ey are more precise at EF, and so the resolution is diﬀerent, as is reﬂected in Eq. 3.18. The automatic rejection and acceptance scheme is the same at EF as for L2.

Offline XS and MET and sumET Algorithms There are several offline reconstruction energy sum algorithms. Out of these, the topo and base algorithms, giving MET topo (sumET topo) and MET base (sumET base), respectively, are closest to the trigger energy sums [116]. As for the trigger, no muon spectrometer information is included in and the difference in detector response with respect to electromagnetic and hadronic energy depositions are not accounted for [117]. In the topo algorithm, so called topological clusters [118] are used. The topological cluster algorithm starts with calorimeter cells, referred to as seeds, with energy Ecell > 4 RMSnoise, where RMSnoise is the root | | × mean square of the signal expected from electronic noise. Next it adds all adjacent cells with Ecell > 2 RMSnoise and finally all neighbouring | | × cells. Only the energy from these clusters are then used to build the MET. Less subtle and therefore less accurate, but more similar to the trigger energy sums, is the base algorithm. The same algorithms are also used for constructing offline sumET . The offline XS is defined as:

MET XS = (3.19) 0.5 (√sumET ) · where MET (sumET ) is MET topo (sumET topo) or MET base (sumET base).

Noise Cuts in the Trigger and Offline Affecting the Relative Values of Energy Sums This section is written as a background to the discussions of the results presented later in this section. The electronic noise is mostly gaussian (or double gaussian) distributed around a mean value, referred to as the pedestal value. The pedestal value is subtracted from all cell (trigger tower) signals at both trigger and offline level. For individual cells the values after subtraction can be slightly different to the true energy deposition, but the discrepancies largely average out for the total energy sums. 72 Chapter 3. ATLAS Level1 Trigger Studies

A so called noise cut is also applied to veto against cells containing pure noise and this differs between different trigger levels and also compared to offline. At L1, L2 and EF, only cells with Etrigger tower > Ecut (L1) or Ecell > Ecut (HLT) are used in the energy sums. Etrigger tower and Ecell are the energy depositions in a trigger tower or cell, and Ecut is the noise cut. This type of noise cut is a 1-sided cut. A 2-sided cut, E > Ecut is instead used in the offline reconstruction. A negative | cell| energy deposition can be measured in a cell arising, for example, from negative electronic noise, undershooting tails from signals from earlier events or from negative filter coefficients used in TileCal. At L1, the E 1 GeV for all trigger towers, see Sec. 2.3. At EF-level the cut cut ≈ value corresponds to three standard deviations of the noise distributions, and the number varies as a function of pseudorapidity between 10 MeV ∼ and 1 GeV. Finally, there is an additional noise cut at L1 for the cells in the FCAL, to account for the differences in the noise distribution. There are several competing contributions to the difference in the energy sums at trigger level and offline, due to these different noise cuts. Firstly, using a 1-sided noise cut will introduce a positive bias because only the positive tail of the noise distribution is included. With a 2-sided noise cut, the negative part of the tail will also be included and the two contributions will cancel each other on the average. Secondly, even if both L1 and EF use 1-sided noise cuts, these will contribute differently to the energy sums compared to the offline value. Thirdly, occasional, very large measured negative energy depositions can, if included in the sums, cancel the energy of a lot of other cells, which will greatly underestimate the total energy sums. In the offline reconstruction, where 2-sided noise cuts are applied, most of the occasional large negative energy values are taken care of by other “cleaning” cuts, as well as in the analysis cuts of a specific physics analysis. The relative impact of the noise cuts also strongly depend on the nature of the energy deposition in a specific event.

W → e + ν Enriched Data

Electron/photon triggered events (Egamma stream) enriched with W → e + ν processes, where the neutrino gives rise to real MET, were used to study the XS and MET trigger efficiencies. The offline selections were a tight electron with pT > 25 GeV and the transverse mass, mT > 40 GeV. The mT is related to the mass of the W and defined using the MET of the event, the electron transverse energy, ET and the electron transverse 3.3. Performance of the MET Significance Trigger 73 momentum:9 q 2 2 2 mT = (MET + ET ) (METx + px) (METy + py) (3.20) − −

Here px and py (METx and METy) are the x and y components of the electron momentum (−−−→MET ). The sumET was required to be > 16 GeV to veto against the occasional large negative energy values in offline energy sums, see Sec. 3.3. Jet cleaning, a procedure for reducing the fake jets in the event, arising for example from hardware problems, non-collision background and cosmic rays, was used [119]. The results showed no significant difference between the topo and base algorithms, and MET topo (sumET topo) alone was therefore used as the main offline MET (sumET ) reference. Like the XS trigger, the electron/photon trigger makes use of the EM calorimeter, thus possibly biasing the XS efficiency. It was however not possible to choose an electron/photon trigger, S, such that Eqs. 3.7 and 3.9 were fulfilled and what is measured is P (T S, c) where T is the XS | trigger and c are the offline selections. The trigger efficiency measured in this way should anyhow give an estimate of the signal efficiency with respect to real MET. It should also be pointed out that the electron/photon trigger and the W e+ν selections might enhance a multijet background. A pion falsely → detected as an electron often contribute to fake MET by mismeasurement in the energy of the fake electron. In Fig. 3.9 efficiencies for L1 and EF XS triggers with different thresholds are shown. The different triggers correspond to different XS value thresholds, XS = 2.0, 2.5, 3.0, 3.5 and 4.0, denoted as XS20, XS25, XS30, XS35 and XS40, respectively. The EF efficiency curves are steeper and reach the plateau faster, which is reasonable when taking into account that the MET Topo is much closer to the EF MET than to L1 MET. The plateaus are stable and > 99.5% for all thresholds, which is the most important feature of the trigger efficiency. The occasional large negative energies at offline allowed by the 2-sided offline noise cut discussed in Sec. 3.3, possibly explains why the plateaus does not reach 100%. This results in that even though the MET can be high at L1 (EF), the XS can still be much smaller than for offline due to the larger sumET , and thus not pass the L1 (EF) XS threshold.

9The distribution looks slightly diﬀerent from the full invariant mass distribution, which is why the cut interval is shifted to lower energies compared to what we would expect from just considering the W mass. 74 Chapter 3. ATLAS Level1 Trigger Studies

(b) Close-up (a)

(d) Close-up

(c)

Figure 3.9: Trigger efficiency for various L1 ((a) and (b)) and EF ((c) and (d)) XS triggers vs MET topo for W e + ν enriched 2011 data events → from the Egamma stream. Double error functions are fitted to data. The figures (b) and (d) are a close-ups of the high XS region of figures (a) and (d), respectively. The different XS triggers shown are described in the text. 3.3. Performance of the MET Significance Trigger 75

W → µ + ν Enriched Data The most detailed study of XS and MET triggers, where collision data were also compared to simulated data, was carried out on events where selections were optimized for choosing W µ + ν events, with real MET → arising from the neutrino. This study contributed to results in the attached paper [1]. The events used in this study are muon triggered events. The muon triggers do not make use of the same parts of the detector as the MET triggers. The two types of triggers are thus assumed to be independent, so that P (T c) = P (T S, c), where T denotes a MET trigger, | | in this case an XS trigger, and S denotes the muon trigger. Periods G - M of 2011 collision data were used in this study and the selections were the following:

EF mu18 MG medium [120]. A trigger chain requiring an EF muon • with pT > 18 GeV. A PV with at least three tracks. This is a standard PV cut. • Jet cleaning. • LarNoise. Cells in EM Calo known to be problematic are removed. • Exactly one so called Staco muon [121] (Staco is a oﬄine muon • reconstruction algorithm) with standard quality cuts and the following properties is required:

– pT > 20 GeV. – η < 2.5. This corresponds to the coverage of the ID which is | | used in the oﬄine muon reconstruction algorithm. p 2 2 – Not overlapping within ∆R = ∆φ + ∆η = 0.1 with any AntiKt4LCTopo [122] jet. The AntiKt4LCTopo is an oﬄine jet reconstruction algorithm.

– 40 GeV < mT < 90 GeV. The transverse mass, mT , is deﬁned in the previous section.

In Fig. 3.10 L1 XS, MET and sumET together with the offline corresponding values are presented, and in Fig. 3.11, the corresponding EF values are shown. The offline XS are in these figures calculated by means of the MET Topo and sumET Topo, explained in Sec. 3.3. In that section, is also the terminology used in explaining these distributions terminology explained. 76 Chapter 3. ATLAS Level1 Trigger Studies

Both the L1 XS (Fig. 3.10a), MET (Fig. 3.10b) and sumET (Fig. 3.10c) show weak correlations centered around y = x with respect to their offline values. A significant contribution to the large differences in these quantities between the L1 and offline values is that the triggers are using reduced granularity, trigger towers, while the offline uses full granularity, calorimeter cells. In addition, the L1 is using analog summing of the energy in the cells, while EF and the offline reconstruction is summing after digitisation. For EF on the other hand, the correlations are much stronger. The EF sumET (Fig. 3.11c) values are offset by 60 GeV, pos- ∼ sibly from the 1-sided noise cut overestimation at EF. This is constant with respect to sumET since it is mostly due to electronic noise and is therefore roughly independent of the real energy deposited. The EF MET distribution (Fig. 3.10b) is centred around y = x. The overestimation of the EF sumET is also clearly visible in the EF XS distribution (Fig. 3.11a) as an underestimation of EF XS, but since this is a constant offset, the effect is most noticeable in the low value region. There are no events in the region below L1 and EF XS 0.7. This is due to the XS calculation ∼ automatic rejections. Fig. 3.12 shows L1 and EF XS distributions for collision and simulated data. The agreement between data and simulation is good. Efficiency curves for various combinations of MET triggers chains for collision data compared to simulation are shown in Fig. 3.13. For each of the figures, the turn-on can be seen to start at the EF level threshold as expected. The data and simulation show good agreement. 3.3. Performance of the MET Significance Trigger 77

(a) XS (b) MET

Figure 3.10: L1 XS (a), MET (b) and sumET (c) vs topo oﬄine values of the same quantity for W µ + ν enriched 2011 collision data. → 78 Chapter 3. ATLAS Level1 Trigger Studies

(a) XS (b) MET

Figure 3.11: EF XS (a), MET (b) and sumET (c) vs topo oﬄine values of the same quantity for W µ + ν enriched 2011 collision data. → 3.3. Performance of the MET Signiﬁcance Trigger 79

6 -1 -1 10 ATLAS Preliminary ∫ L dt = 4.3 fb , s = 7 TeV 106 ATLAS Preliminary ∫ L dt = 4.3 fb , s = 7 TeV Events Events 105 105

4 104 Data 2011 10 Data 2011 MC W → µ ν MC W → µ ν 3 103 10

2 2 10 10 10 10 1 1 0 5 10 15 20 25 0 5 10 15 20 25 L1 XS EF XS

Figure 3.12: L1 (left) and EF level (right) XS distributions for simulated W µ + ν events compared with data. → 80 Chapter 3. ATLAS Level1 Trigger Studies

1 1

Efficiency ATLAS Preliminary Efficiency ATLAS Preliminary 0.8 0.8 Data 2011 Data 2011 0.6 MC W → µ ν 0.6 MC W → µ ν

0.4 miss 0.4 miss L1 ET > 10 GeV L1 ET > 20 GeV miss miss EF ET > 20 GeV EF ET > 30 GeV 0.2 0.2 ∫ L dt = 4.3 fb-1, s = 7 TeV ∫ L dt = 4.3 fb-1, s = 7 TeV

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T

1 1

Efficiency ATLAS Preliminary Efficiency ATLAS Preliminary 0.8 0.8 Data 2011 Data 2011 0.6 MC W → µ ν 0.6 MC W → µ ν

0.4 miss 0.4 miss L1 ET > 30 GeV L1 ET > 35 GeV miss miss EF ET > 40 GeV EF ET > 50 GeV 0.2 0.2 ∫ L dt = 4.3 fb-1, s = 7 TeV ∫ L dt = 4.3 fb-1, s = 7 TeV

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T

1 1

Efficiency ATLAS Preliminary Efficiency ATLAS Preliminary 0.8 0.8 Data 2011 Data 2011 0.6 MC W → µ ν 0.6 MC W → µ ν

0.4 miss 0.4 miss L1 ET > 40 GeV L1 ET > 50 GeV miss miss EF ET > 60 GeV EF ET > 70 GeV 0.2 0.2 ∫ L dt = 4.3 fb-1, s = 7 TeV ∫ L dt = 4.3 fb-1, s = 7 TeV

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T Figure 3.13: Comparison of measured and simulated combined all-level trigger efficiency for various MET triggers for W µν events vs the → offline MET topo. The thresholds of x GeV, of the triggers at L1 (EF) miss level are given in the figures as L1 (EF) ET > x. 3.3. Performance of the MET Significance Trigger 81

Conclusions and Further Developments

The XS trigger was simulated and studied for events enriched in W e+ν → and W µ + ν, where real MET from the neutrino is present. It was → shown to be stable, showing good signal efficiency and behaving as expected. The turn-ons were positioned at places expected with respect to the different thresholds, and the plateaus showed high efficiency. As expected, EF trigger efficiencies were higher than L1 efficiencies, and the EF quantities showed better correspondence with the offline values compared to L1 quantities. In Ref. [1] the XS trigger is shown to behave robustly even for the highest pile-up conditions of 2011. Fig. 3.14 shows the trigger rate per bunch crossing as a function of µ for MET and XS triggers. It is apparent that the XS triggers are mostly independent of pile-up for large µ values, whereas MET triggers show a strong dependence on µ.

ATLAS Preliminary 2011 G ATLAS Preliminary 2011 G 102 102 s = 7 TeV 2011 H s = 7 TeV 2011 H 2011 I 2011 I 10 2011 J 10 3.0 2011 J 20 GeV 2011 K 2011 K 1 2011 L 2011 L 1 2011 M 4.5 2011 M 10-1 40 GeV 10-1 10-2 6.0 10-2 70 GeV 7.5 10-3 Unprescaled rate / colliding bunch [Hz] Unprescaled rate / colliding bunch [Hz] 10-3 0 5 10 15 20 0 5 10 15 20 µ µ

Figure 3.14: Comparison of trigger rates as a function of the average number of interactions µ per bunch crossing for periods G - M during 2011. The left plot shows MET triggers and the right shows XS triggers. The thresholds are given in the ﬁgures, to the left of the data points. The ﬁgures are taken from Ref. [1].

With increasing pile-up the sumET and fake MET from soft scatterings increase and fake MET from multijets events with high pT as well as any real MET will become less and less important in contributing to the XS value. This means that the eﬀective MET threshold for real MET (and high fake MET) will increase, which is visible in Fig. 3.14 where the trigger rates even decrease for high XS thresholds as a function of µ. The XS trigger chains XS30, XS45, XS60, XS75 and XS100, where the number indicates the EF XS threshold 10, were introduced in 2011 × 82 Chapter 3. ATLAS Level1 Trigger Studies and XS triggers have also been used in combination with other triggers. The low threshold MET triggers had to be kept, since the eﬀective MET threshold for XS triggers increase with pile-up, as discussed above.

3.4 L1 Trigger Upgrade Studies

Background and Setup

The sensitivity of the sumET and MET triggers to in-time pile-up, motivates the evaluation of new trigger variables. Studying the behavior of various final-states at different levels of pile-up in the plane of sumET +MET vs sumE, it was found that the data points of one specific (fake) MET topology follow a straight line as a function of pile-up, see Fig. 3.15. The offset of these lines are different but the slope is close to constant. A new variable is then constructed out of the linear combination of sumE and sumET +MET corresponding to the vector which is orthogonal to these lines. This variable would then be pile-up independent.

Figure 3.15: Profile histogram of offline sumET + MET vs sumE for simulated data of different (fake) MET topologies and collision data, together with fitted linear functions.

Taking this a step further and studying this variable in terms of the trigger variable XS, will give a surprisingly good separation for generic topologies that would mix terribly as a function of just sumE, sumET or MET. 3.4. L1 Trigger Upgrade Studies 83

For these new trigger variables to be implementable, sumE would also have to be accessible at L1 (an overview over the L1 calorimeter trigger and all its components is given in Sec. 2.3). This was at the time of this study (and is presently still) not the case. For the electromagnetic calorimeter, the conversion of the energy, E, to transverse energy, ET , is carried out in two steps. An approximate adjustment happens at the calorimeter front-end where the gain is altered between 1 and 3.5, depending on the trigger tower pseudorapidity. A more precise correction is then made at the Receiver, where the final amplification is carried out. For the hadronic calorimeter the ET conversion will be performed only by the Receiver. In this study I investigated how an inclusion of sumE to L1 could be done by implementing a ET E conversion in the JEMs, where → the sumET and MET sums are built. Other approaches to solving this problem had been discussed before. However since the hardware setup is optimized for the present information flow, and conversion to E means larger values, all solutions involve precision losses of the energy. The first conversion to transverse energy for the electromagnetic energy happens in the Layer Sum Boards (LSB), located on the calorimeter front-ends, where the conversion is carried out by adjustable resistors. Next the (still analog) signals are transmitted to the TBBs. Were one for example to remove the conversion here, and send the total energy instead of the transverse energy, the Receiver would not be able to maintain the present precision, since it is built for the energies in the ET range. To keep the precision, pseudorapidity-dependent Receivers would then be required. Transforming from transverse to full energy at the JEMs, where sumE could then be built, would also infer that the loss of precision of 1 GeV in ET , would propagate to a loss of up to 3 GeV in E for η = 3.2 (max- imal pseudorapidity for the calorimeter), but would not require any new hardware to be implemented.

L1 Hardware Emulation

To evaluate the performance of the new trigger variable, a hardware simulation of a ET E conversion in the JEMs was carried out. The input → to the JEMs are 9 bit jet elements, in GeV counts. This means that the LSB represents 20 = 1 GeV. These values are available in the data from ATLAS as integers. For each jet element, a conversion from ET Ex/Ey → is carried out using the η and φ from the jet element. For cosine and sine 84 Chapter 3. ATLAS Level1 Trigger Studies factors, 12 bit integer data types are used to approximate ﬂoating numbers (32 bits). The largest integer number that can be represented with 12 bits is 4095 and the cosine and sine factors, which will have values between 0 and 1, are mapped to values between 0 and 4095. In the emulation, a ﬂoating point data type was used for these cosine and sine factors. The Ex and Ey values are represented as 14 bit numbers with 0.25 GeV counts. To emulate this, the Ex/Ey were truncated to a precision of 0.25 GeV. At this stage, the proposed ET E conversion would take place. The → following procedure was emulated, where the new proposed procedures are given in italics:

For each JEM: • 10 – Summing of Ex, Ey and ET , excluding FCAL.

– L1 hardware reduces the 14 bit Ex and Ey to 12 bits, giving 1 GeV/count instead of 0.25 GeV/count.

– Converting of ET to E using ﬂoat type conversion factors.

– In preparation for transferring the Ex/Ey/ET signals to the CMMs, a quadlinear compression11 is carried out. – In preparation for transferring the E signals to the CMMs, a quadlinear compression is carried out.

– Transferring the Ex/Ey/ET value to the corresponding CMM. – Transferring the E value to the corresponding CMM.

For each CMM: •

– Summing of Ex/Ey/ET (over JEMs) is performed. – Summing of E (over JEMs)

10FCAL covers the forward region η > 3.2 of the electromagnetic calorimeter where thus pseudorapidity is large and the conversions factors accordingly are too. The η precision is much worse here than in the rest of the calorimeter, because FCAL is using another custom placeholder coordinate for the trigger tower, which does not have to coincide with the trigger tower centre. (Some towers span up to 1.5 in η). Since the uncertainty of the energy obtained from conversion from ET obviously is very much larger than for the rest of the calorimeter, FCAL was chosen to be excluded in this study. 11The quadlinear compression was emulated by Alan Watson. 3.4. L1 Trigger Upgrade Studies 85

The L1 hardware calculates MET by inserting Ex and Ey values into a LUT. The simulation of this procedure is described in Sec. 3.3. If Ex or Ey overﬂow the LUT input values, the sumET + MET is set to 5500 GeV, to be able to identify these events.

Results

In Fig. 3.16 the simulated of L1 sumET + MET and L1 sumE for 2011 collision data enriched in various different final states. W e + ν events → are selected from the Egamma stream by requiring precisely one offline tight electron with pT > 25 GeV and transverse mass mT constructed with the MET, such that mT > 40 GeV. Randomly triggered events were used to get minimum bias events. The minimum bias trigger chain used was EF rd0 filled NoAlg (EF level), L2 rd0 filled NoAlg (L2), L1 RD0 FILLED (L1). More information on minimum bias triggers can be found in Ref. [123]. To obtain events including one or more high pT jets, events passing single high pT jet trigger chains or high pT multi-jet triggers, were chosen. The trigger chains used are presented in Tab. 3.4. The nomenclature is that for example for the EF 3j30 a4tc EFFS trigger, 3 jets with pT > 30 GeV are required at EF level. This trigger is proceeded by L1 3J10 at L1, which requires 3 jet candidates (see Sec. 2.3) with ET > 10 GeV and sends RoIs (see Sec. 2.3) to L2, where the L2 trigger uses a more sophisticated algorithm to identify jet candidates. If 3 such candidates with ET > 25 GeV are found, the L2 3j25 is passed. At the EF level, a full scan (EFFS) of the RoIs is performed. Topological clusters [118] (tc) (see Sec. 3.3) of calorimeter cells are used as input to the so called anti-kT algorithm [122] with distance parameter R = 0.4 (a4). More information about the trigger algorithms can be found in Ref. [124]. For all data, tight jet cleaning and removal of events with jets in transition regions were imposed. A simple qualitative interpretation of Fig. 3.16a can be summarized as follows. There is a close to linear behaviour for minimum bias and W e+ν triggered events for sumE < 900 GeV and sumE < 1500 GeV, → respectively, possibly with the same slope. For high pT jet triggers, it is not clear from this figure whether any linearity exists, which is also the case for multijet triggered events shown in Fig. 3.16b. A possible linearity could also exist but be characterized by different slopes in different sumE regions. 86 Chapter 3. ATLAS Level1 Trigger Studies

(a) W eν, minimum bias and single high jet pT events selected as described in the text.→

(b) W eν, minimum bias and several high pT multi-jets events. In the label, it says→ from the top: “W eν”, “Min. Bias”, “EF 3j30 a4tc EFFS”, “EF 4j30 a4tc EFFS”, “EF 5j30 a4tc→ EFFS”, “EF 6j30 a4tc EFFS”, “EF 4j55 a4tc EFFS or EF 3j75 a4tc EFFS”. The triggers are described in the text.

Figure 3.16: Simulated L1 SumET + MET vs sumE for differents types of events. The figures are profile histograms. The data used is described in the text. 3.4. L1 Trigger Upgrade Studies 87

Single high pT jet triggers EF trigger L2 trigger L1 trigger EF j100 a4tc EFFS L2 j95 L1 J75 EF j75 a4tc EFFS L2 j70 L1 J50 EF j55 a4tc EFFS L2 j50 L1 J30

High pT multi-jet triggers EF 3j30 a4tc EFFS L2 3j25 L1 3J10 EF 4j30 a4tc EFFS L2 4j25 L1 4J10 EF 5j30 a4tc EFFS L2 5j25 L1 5J10 EF 6j30 a4tc EFFS L2 6j25 L1 6J10 EF 4j55 a4tc EFFS L2 4j50 L1 4J30 or EF 3j75 a4tc EFFS L2 3j70 L1 3J50

Table 3.4: Trigger chains used to select high pT jet events. The top table presents triggers requiring one high pT jet and the bottom requires several. The nomenclature is described in the text.

There is a visible separation between W e + ν triggered events → and high pT jet and multijet triggered events. To be able to quantify the results, more statistical precision would be needed.

Summary and Further Development An implementation of sumE into L1 hardware and software has been emulated. A first check evaluation of the possible separation of different event topologies in the plane of sumE and sumET +MET, as well as a possible linearity, earlier seen at offline reconstruction level, has also been carried out. The results were not convincing enough to lead to an implementation or further evaluation at the time of the study. 88 Chapter 4

Highly Ionising Particle Detector Response

4.1 HIPs in the ATLAS Detector

HIPs have distinct measurable signatures in ATLAS. As described in Sec. 2.3 the HIPs will give rise to a large number of HT TRT hits. In the EM Calo, the HIP ionisation of the detector material results in a very concentrated energy deposition, unlike that of showering particles like electrons. The HIPs will saturate the Pixel detector. The saturated pixels were by the time of the data-taking of the research presented in this thesis not read out and this signature could accordingly not be used.

4.2 Energy Deposition

HIPs in the energy regime of the search presented in this thesis deposit energy in a medium they traverse dominantly through ionisation or excitation of the atoms of the medium. In a particle detector, this energy is for example measured through the liberated electrons or the scintillation light emitted by the excited material [125]. HIPs may also collide with the atomic nuclei in a material and loose energy through what is referred to as Non-Ionising Energy Loss (NIEL) [126]. The NIEL is however also negligible in comparison to the ionisation loss in particle detectors [36]. The mean ionisation or excitation energy deposition per unit length in the energy and velocity range relevant to the HIPs sought in this thesis, depends on the charge and speed of the HIP and the properties of

89 90 Chapter 4. Highly Ionising Particle Detector Response the material1, but is independent of the HIP mass. Eqs. 4.1[7] and 4.2[127, 128, 129] below give the mean energy deposition of HECOs and monopoles, respectively. For HECOs the equations are valid in the range 0.1 . βγ . 1000, and for monopoles in the range 0.1 . βγ . 100.

2 2 2 2 dE Z z 2mec β γ δ(βγ) = K ln β2 (4.1) − dx A β2 I − − 2

2 2 2 dE Z 2mec β γ k(g) 1 δ(βγ) = K g2 ln + B(g) (4.2) − dx A I 2 − 2 − 2 − where k is the KYG correction : ( 0.406, n 1 k(g) = | | ≤ (4.3) 0.346, n 1.5 | | ≥ and B is the Bloch correction:2 ( 0.248, n 1 B(g) = | | ≤ (4.4) 0.672, n 1.5 | | ≥ The HECO charge is denoted by z, and the monopole charge by g, giving the multiples of the elementary charge e and the Dirac charge gD, respectively. The parameter β is deﬁned as β = v/c where v is the speed of the particle and c is the speed of light and γ is the Lorentz factor of the HIP. The atomic number of the material is represented by Z and the −1 2 2 atomic mass by A. The constant K = 0.307 MeV mol cm and mec is the electron mass in MeV. The mean excitation energy of the material, I, is a constant, given in eV, and values for diﬀerent materials are given in Ref. [130]. The δ(βγ) is referred to as the density correction and is described below. The equations are expressed in MeV cm2g−1. Other parametrizations are required when the HIP speed approaches those of orbital electrons, βγ . 0.1. For HECOs, the model used is described in Ref. [131]. The energy loss of monopoles is in this region is monotonically increasing with velocity and in this search an interpolation

1The dependence on the material is weak, as Z/A is 0.5 for most materials. ∼ Exceptions are hydrogen and very heavy materials [125]. 2 The k and B corrections are in the references given for charges gD and 2 gD and has here been generalised to fractional charges by using the values for gD also for 0.5 gD and the values for 2 gD for 1.5 gD. 4.2. Energy Deposition 91

/g] + 2 µ on Cu 100 µ Bethe Radiative Anderson- Ziegler Radiative effects Eµc 10

Scharff reach 1%

Lindhard- Radiative Minimum losses ionization Nuclear losses Stopping power [MeV cm Without 1 4 5 0.001 0.01 0.1 1 10 100 1000 10 10

0.1 1 10 100 1 10 100 1 10 100 [MeV/c] [GeV/c] [TeV/c] Muon momentum

Figure 4.1: Mean energy deposition per unit length of positive muons traversing copper as a function of βγ. Solid curves indicate the total stopping power. Data below the break at βγ 0.1 are taken from Ref. [131], ≈ and data at higher energies are from Ref. [132]. Vertical bands indicate boundaries between different approximations. The short dotted lines labeled µ− illustrate the “Barkas effect” the dependence of stopping power on projectile charge at very low energies [133]. dE/dx in the radiative region is not simply a function of βγ. This figure is taken from Ref. [7].

between the value of the energy loss at βγ = 0 and at βγ = 0.1 is used [128]. At high velocities, βγ & 100 for monopoles and βγ & 1000 for HECOs, radiative eﬀects such as Bremsstrahlung need to be taken into account [128,7]. This velocity regime is however outside the energy range of the HIPs produced in the search presented in this thesis. For example, a HIP of mass 200 GeV would have to have a kinetic energy of 20 TeV to reach βγ = 100. In Fig. 4.1, the mean energy deposition for muons in copper (Eq. 4.1) is shown for a large range of βγ. The energy loss is characterised by a decrease in ionisation 1/β2 until a minimum is reached at βγ 3, ∼ ∼ whereafter a logarithmic rise begins. Along with a higher particle kinetic 92 Chapter 4. Highly Ionising Particle Detector Response

103 10 /g) /g) 2 2 Ahlen, |g|=g Bethe, |z|=68.5 9 D Be 8 Be Al Al 7 2 Fe Fe 10 Pb 6 Pb

dE/dx (GeV cm dE/dx (GeV cm 5 4 3 10 2 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 β β

Figure 4.2: Mean ionisation (excitation) energy loss for HECOs (left) and monopoles (right) as a function of the speed β for diﬀerent materials as marked in the ﬁgure.

energy, its transverse electric field is extended, which means more and more distant collisions play a role, causing this so-called relativistic rise. The density effect correction, δ, is introduced to describe the polarisation of the media limiting this effect [134]. It is dependent on the particle energy as well as the material.3 For monopoles, the mean energy deposition formula has been computed using different techniques for close-collision and distant-collisions. The close-collision monopole energy loss has been computed by using the Dirac equation for an electron moving in the magnetic field resulting from a fixed monopole [135]. The distant-collision contribution was computed with a semi-classical approach using classical macroscopic electrodynamics [136]. Comparing Eq. 4.1 and Eq. 4.2, the properties of the mean ionisation (excitation) energy deposition of monopoles is strikingly different from that of HECOs. This can also be seen4 by comparing the left graph in Fig. 4.2, showing the energy loss for HECOs of charge 68.5 e, to the right graph in the same figure, showing the energy loss for a monopole of charge 1 gD. Firstly it can be noted that the energy loss for monopoles increases for the whole range of β. This is due to the fact the Lorentz force for a monopole affected by an electric field increases with the monopole speed, see Eq. 1.40. Secondly, the ionisation for HECOs and monopoles with the

3This is more important for liquids and solids than for gases. 4Features like the logarithmic rise and position of the minimum are only visible when studying the energy loss as a function of βγ and thus not visible in Fig. 4.2. 4.3. δ-ray Production 93 same strength of the coupling are only comparable in magnitude for high velocities β & 0.8. The theory of energy deposition described above is implemented as part of the GEANT [137] package to describe HECO and monopole interactions in the ATLAS detector.

4.3 δ-ray Production

δ-rays are low-energy inner shell electrons that are liberated from the atoms of the detector material. Being the result of close-collision interaction they carry a non-negligible amount of kinetic energy. The δ-electrons account for up to 30% of the HIP energy deposition [138]. The δ-ray production is modelled within Equations. 4.1 and 4.2. The maximum energy of a δ-electron, Eδ,max, is given by [7]:

EHIP,kin EHIP,kin Eδ,max = 2me + 2 (4.5) mHIP mHIP

Inserting the values for a monopole with mHIP = 1000 GeV and EHIP,kin = 1000 1500 GeV for which is the acceptance for the search described in − Chap.5 is high, a maximum energy of 3 5 MeV is obtained. At such − energies, electrons will not emit any transition radiation. Electrons starts yielding HT TRT hits through transition radiation at around 1 GeV in the TRT [139]. However the combined energy deposition of several δ- electrons through ionisation will result in HT TRT hits, typically in a 1-cm-wide region along the HIP path, see Sec. 2.3. Since the fraction of HT TRT hits is used as a discrimination variable in the search described in Chap.5, the modelling of the contribution of δ-rays and its interaction with TRT is important for this search. The Geant4 [137] response of the TRT has been validated. In the EM Calo, δ-rays will ionise the argon directly and thus contribute to the energy deposition. If their energies are high enough, they could in addition shower and thus compromise the distinct narrow energy deposition of HIPs in the EM Calo. For a monopole of mass 200 GeV and and EHIP,kin = 1000 GeV, Eδ,max = 35 MeV which in the regime where the Bremsstrahlung cross section exceeds that of ionisation [7]. As described in Sec. 5.3, a degradation of the discriminating variable w is seen for low mass HIPs. 94 Chapter 4. Highly Ionising Particle Detector Response

4.4 Recombination and HIP Correction to Birks’ Law

HIPs traversing the EM Calo ionise the liquid argon atoms and the liberated electrons are detected. As HIPs give rise to a very high ionisation density, electron-ion pairs may recombine and the electron and the preceding energy deposition by the HIP is left undetected. This recombination is described by Birks’ law [140, 141, 142, 143, 144, 145]:

0 1 + A k/ED Evis = E0 , (4.6) 1 + k/(ρED)dE/dx relating E0, the true deposited energy, to Evis, the detected, visible energy. Here dE/dx is the energy deposited per unit length, and ρ is the density of the liquid argon. The voltage of the drift electric field, ED, is assumed to be a uniform 10 kV/cm. Birks’ constant, k, is taken to be k = 0.0486 (kV/cm)(g/cm2)(1/MeV).5 The parameter A0 = 1.51 is a normalisation parameter obtained by comparing the ATLAS simulation to test beam electron and pion data [146, 147]. The recombination effect is smaller for a large drift electric field strength, as a larger electric field accelerates the electrons and ions away from each other. A higher energy deposition, which is a measure of the ion density, results in a larger recombination. HIP k 12

0 0 2000 4000 6000 8000 10000 12000 dE/dx [MeV/cm]

Figure 4.3: The HIP correction to Birks’ law, kHIP , as a function of dE/dx for various heavy ions for ED =7 kV/cm, where ED is the voltage of drift electric ﬁeld.

5The value of k is measured by the ICARUS TPC collaboration [144] using cosmic- ray muons and protons. 4.5. Magnetic Field Deviation 95

Eq. 4.6 requires a correction for particles with large dE/dx values, for which the recombination effects are otherwise overestimated. In Ref. [138] it is described how this correction, kHIP , was obtained by comparing published heavy-ion data to a Geant4 [137] simulation of heavy ions in a liquid argon calorimeter. Using the correction factor kHIP a corrected 0 visible energy for HIPs, E = kHIP Evis is obtained. The δ-ray energy vis · deposition is unaffected by recombination effects. The ratio of the visible energy to the true energy of δ-electrons and the HIPs, respectively, must therefore be separated in the simulation. Fig. 4.3 shows the applied correction.6 Birks’ law as given Eq. 4.6 and the HIP correction to it was implemented in the ATLAS simulation 2010.

4.5 Magnetic Field Deviation

HIPs are bent in the 2 T magnetic field present in the ID of the AT- LAS detector, see Sec. 2.3. This is a substantial effect for low masses and high charges. A considerable bending compromises the HIP’s narrow energy deposition in the EM Calo. The energy lost or gained by a HIP by the magnetic field is however negligible compared to that due to ionisation [148]. The magnetic field is directed along the beam axis, which means that a HECO will be deviated in the r-φ-plane only, where it makes a circular motion. The monopole will instead be accelerated in the z-direction, see Eq. 1.40, following a parabola in the r-z-plane [78, 36]:

g20.54 B r2 r z(r) zv = 0.5 | | + (4.7) − 2pT βT tan θ0 where g is the charge of the monopole in units of the Dirac charge, zv is the vertex position, pT and βT are the transverse momentum and transverse velocity and θ0 is the angle between the monopole’s initial direction and the z-axis. The trajectories of HIPs is simulated by Geant4.

6The correction is taken as constant for dE/dx > 12000 MeV/cm, as a result of low statistical precision in the experimental data used to obtain the correction. 96 Chapter 5

Search for Magnetic Monopoles and HECOs at ATLAS

This chapter concerns the research given in Paper II. First, a short introduction to the analysis will be given. The simulations, the event selection and the signal efficiency will then be discussed. This is followed by an overview of the systematic uncertainties and a discussion of the background estimation. The statistical procedure will then be presented, and finally the results will be given. While this chapter aims to give an overview of the full analysis, most emphasis is placed on those parts for which I had a major responsibility. These were event generation of HECOs, the pT cuts for event generation based on the trigger efficiency, an algorithm finding high signal efficiency (so called fiducial) regions, cut- flows and the statistical procedure for limit setting.

5.1 Introduction

Stable massive particles are important observables in the search for new physics, as they are predicted by many BSM models. This search is for two types of particles in the mass range of 200 GeV - 2500 GeV: monopoles and HECOs, see Sec. 1.3. Monopoles and HECOs are collectively referred to as Highly Ionising Particles (HIPs), due to the high electromagnetic energy loss that both types of particles suﬀer when interacting with detector material, see Sec. 4.2. The search has been conducted using a 2012 ATLAS dataset of proton-proton collisions at 8 TeV corresponding to an

97 98 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS integrated luminosity of 7.0 fb−1. A representation of a simulated ATLAS event of a monopole is given in Fig. 5.1.

Figure 5.1: A simulated ATLAS event of a single monopole of mass 1000 GeV and charge 1.0 gD. The brown diagonal line represents the beam line and the green towers represent the energy deposits in the EM Calo. The white dots are LT TRT hits and the red points aligned with the large EM energy deposition are the HT TRT hits hits associated with the monopole trajectory.

5.2 Simulations

Simulated samples were used in this analysis to study signal acceptances and background signatures. A full detector simulation has been developed for this search in Geant4 [137, 149], based on work done for the previous monopole search at ATLAS [75]. The simulation describes the interaction of the HIPs with the magnetic field and includes special routines relating to the propagation of monopoles (see Sec. 4.5). Energy loss, which is dominated by ionisation in the detector material, is modelled using theoretical predictions described in Secs. 4.2- 4.4. It includes δ-ray production and recombination effects. A pile-up simulation reproducing the collision data conditions was also included. Two types of samples were produced. Due to the non-perturbative nature of the HIP coupling to the photon, production models suffer from large uncertainties (see Sec. 1.3) motivating the production of a set of single particles (SP) for setting model-independent limits, see Sec. 5.4 5.2. Simulations 99

Figure 5.2: A Feynman diagram for the production of a monopole- antimonopole pair via a Drell-Yan-like mechanism. The (anti)monopole is denoted as m ( ¯m),the protons as p, the (anti)quark as q (¯q),the virtual ∗ photon as γ and the couplings as αem and αmm for the electromagnetic coupling between the quarks and the photon and the coupling between the photon and monopoles, respectively.

and Sec. 5.8. The set was produced assuming a flat distributions in pseudorapidity, η, and kinetic energy, Ekin, and in the ranges η < 3.0 and | | 10 GeV < Ekin < 3000 GeV. The other type of dataset was produced using a simplified (leading order, photon-coupling only) Drell-Yan-like (DY) pair-production model [2], see Fig. 5.2, in order to obtain a different kinematic distribution.

Both sets of samples were produced with all combinations of HIP masses of 200, 500, 1000, 1500, 2000 and 2500 GeV, and HIP charges of 0.5, 1.0, 1.5 and 2.0 gD for monopoles and charges 10, 20, 40, and 60 e for HECOs. The DY and SP samples contain 20 000 and 50 000 events, respectively.

To study the distributions of selection observables, two sets of background events were used. Electroweak samples, produced with

Powheg [150] and Pythia8 [151], consist of p + p W eν + X, → → p + p γ e+e− + X and p + p Z e+e− + X processes. Jet → → → → production samples, produced with Pythia8, contain two jets with a total pT cut-oﬀ at 1000 GeV and only account for a fraction of the multijet background in our data, which is dominated by events with lower pT . The background samples are therefore only used to help to understand the possible processes which contribute to the background. To estimate the background in the signal region, a data-driven technique is used. 100 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

Signal Event Generation

The Monte Carlo (MC) matrix element calculator and event generator MadGraph5 [152] was used to generate DY signal samples, with CTEQ6L1 [153] parton distribution functions and Pythia8.175 [154, 151] for hadronisation and modelling of the underlying event. Event generation validation was carried out using kinetic distributions of the observables relevant to this work. Fig. 5.3 shows distributions of transverse momentum, kinetic energy, speed β as well as the pseudorapidity, for DY HECOs of charge 40 e and various masses, where cuts on pT (described in the next section) have been applied. The cuts are clearly visible in the transverse momentum distributions, where it also can be seen that the higher masses in general have a larger pT and lower velocity. The pseudorapidity distributions show that HECOs with larger masses are more central, as expected.

Figure 5.3: Generator-level observables for DY-produced HECOs of charge 40.0 e and diﬀerent masses, where pT cuts have been applied. Dis- tributions are shown of transverse momentum pT , kinetic energy Ekin, speed β and pseudorapidity η distributions. 5.3. Event Selection 101

Generator Level pT Cuts To increase the simulation efficiency, that is to minimise the fraction of events containing HIPs which lie outside the range of acceptance, generator-level cuts on the HIP pT were applied to the DY samples. The cuts were based on the visual inspection of trigger efficiency (see Sec. 5.3) distributions for single particles, the trigger being the dominant contribution to the topology of the signal efficiency. Examples of pT cuts are given in Tab. 5.1. The corresponding set of trigger efficiency distributions, representative for all samples, are shown in Fig. 5.4 and are explained in Sec. 5.3.

Charge [e] pT threshold [GeV] Charge [gD] pT threshold [GeV] 10 200 0.5 150 20 150 1.0 250 40 200 1.5 350 60 300 2.0 650

Table 5.1: Generator-level pT thresholds for DY HECOs (left) and DY monopoles (right) of mass 1000 GeV and various charges.

5.3 Event Selection

Introduction The HIP signature is described in Chap.4 and in Sec. 2.3. It is different from the well known signatures reconstructed in ATLAS such as those due to electrons or jets, and requires a dedicated search with a bespoke HLT HIP trigger and custom selection variables. A HIP candidate is in this analysis represented by a calorimeter cluster (trigger RoI) and an associated region in the TRT. The analysis selections will be imposed on these objects. The HIP trigger will be introduced in the next section, followed by the so called preselection, aiming at making a finer selection of candidates in the events selected by the trigger. Next, selections on for example the EM Calo cluster energy and the pesudorapidity will be described, and finally the final discrimination variables associated with the HIP signature in the EM Calo and TRT will be presented. Cut-flows for HIPs of mass 1000 GeV and various charges are shown in Figs. 5.7 and 5.8. The selections given in the figures are described in the following sections. 102 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

Possible backgrounds are high-pT electrons or multijet processes. The L1 trigger used in this search is designed to find electrons. Ultra-relativistic electrons also result in a high number of HT TRT hits. High-pT jets can give a similar signature in the EM Calo, since pions in the jet can mimic electrons through π0 γγ resulting in an EM Calo cluster which could → be associated with a track in the inner detector from any of the charged particles in the jet. The multijet background firing the HIP trigger can in addition to electrons result in a HT TRT fraction because of random combinations of HT TRT hits from different particles within the jet.

Trigger

A general description of the ATLAS trigger system is given in Sec. 2.3.A custom made HLT (L2 and Event Filter) trigger, EF_g_nocut_hiptrtL2 [2], has been developed. It has three principal advantages increasing the sensitivity significantly in comparison with using a full electron-photon trigger chain which would be the best alternative in the absence of a bespoke trigger. In contrast to the HLT electron/photon trigger, the HIP trigger cluster reconstruction does not require energy deposition in the second EM Calo layer, it has a lower energy threshold and also makes use of TRT hit information. Since no track information is available at L1, the HIP trigger could only be developed for HLT. The HLT HIP trigger is seeded from an L1 electron/photon trigger, L1_EM18VH, which was the lowest unprescaled electron/photon trigger during 2012. It has variable ET thresholds between 18 and 20 GeV and a veto against energy deposition of > 1 GeV in the HadCore (see Sec. 2.3). The development of its predecessor is described in Sec. 3.2. At least one RoI has to fulfil these requirements for the L1_EM18VH to be fired, but all L1 RoIs in a L1 triggered event are considered in the EF_g_nocut_hiptrtL2 algorithm. Extending from the IP, a wedge of 0.015 rad in φ is built around an ± L1 EM Calo RoI, defining an associated region in the TRT. The number of LT TRT hits, NLT,trig and HT TRT hits, NHT,trig, are counted in this region and the following requirements are imposed on the NHT,trig and the fraction of high threshold hits, fHT,trig, in order to fire the HIP trigger:

NHT,trig > 20 •

NHT,trig/(NHT,trig + NLT,trig) = fHT,trig > 0.37 • 5.3. Event Selection 103

The acceptance of the L1_EM18VH is the dominant contribution to the overall acceptance of the EF_g_nocut_hiptrtL2 (see Fig. 5.4). Two basic effects drive the L1_EM18VH trigger efficiency for HIPs. HIPs are required to reach the EM Calo to be able to fire the trigger and HIPs traversing the EM Calo into Tile can fire the hadronic veto. The rise of the trigger efficiency is governed by the first factor and the fall-off by the second. In general, higher charges ionise more and therefore need more energy to travel through the ID material and reach the EM Calo, or penetrate the EM Calo and reach the Tile. This is visible in all the trigger efficiency distributions, showing later turn-ons and longer plateaus for higher charges. HIPs reaching the end-caps have traversed more material and thus more energy is required to reach the EM Calo, see Sec. 3.2. This is however not visible in the distributions in Fig. 5.4 since the x-axes show transverse momentum and not the total momentum, even if the general loss in efficiency compared to the barrel region for a specific mass and charge can be seen. Monopoles of charge 0.5 gD and HECOs of charge 20 e, which are comparable in the amount of energy they lose due to ionisation, show similar properties with some exceptions. The HECOs have a wider plateau, possibly due to the high ionisation energy loss at the end of their path where they are at low speed. No velocity information is however available after the HIPs have been produced and comparing monopoles and HECOs is not straightforward. Comparing the bottom left distribution in Fig. 5.4 to Fig. 5.5, where the latter shows an example of the trigger efficiency with a hadronic veto emulating that of the trigger applied offline, suggests that the modelling of the veto in the trigger simulation is unsatisfactory1. This is used to explain the efficiency peaks after the fall-offs, visible for low charges. To model the efficiency correctly, an offline hadronic veto is used in the selection requirements, see Sec. 5.3.

Preselection The preselection aims at selecting HIP candidates in an EF_g_nocut_hiptrtL2 triggered event, and does not reject any events. Preselection candidates are constructed from an oﬄine reconstructed topological calorimeter cluster [118] and an associated region in the TRT. The topological cluster algorithm is described in Sec. 3.3.

1Since the trigger information in reconstructed data is limited, the hadronic veto applied oﬄine is an approximation of that applied in the L1 trigger. 104 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

1.2 1.2

m = 1000 GeV, q = 10 e m = 1000 GeV, q = 10 e m = 1000 GeV, q = 20 e m = 1000 GeV, q = 20 e 1 m = 1000 GeV, q = 40 e 1 m = 1000 GeV, q = 40 e m = 1000 GeV, q = 60 e m = 1000 GeV, q = 60 e

0.8 0.8

0.6 0.6 Fraction of events passing trigger Fraction of events passing trigger 0.4 0.4

0.2 0.2

0 0 0 500 1000 1500 2000 2500 3000 3500 4000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 p [GeV] p [GeV] T T

1.2 1.2

m = 1000 GeV, q = 0.5 gD m = 1000 GeV, q = 1.0 gD 1 1 m = 1000 GeV, q = 1.5 gD m = 1000 GeV, q = 2.0 gD m = 1000 GeV, q = 0.5 gD 0.8 m = 1000 GeV, q = 1.0 gD 0.8 m = 1000 GeV, q = 1.5 gD m = 1000 GeV, q = 2.0 gD 0.6 0.6 Fraction of events passing trigger Fraction of events passing trigger 0.4 0.4

0.2 0.2

0 0 0 500 1000 1500 2000 2500 3000 3500 4000 0 200 400 600 800 1000 1200 1400 1600 p [GeV] p [GeV] T T

Figure 5.4: EF_g_nocut_hiptrtL2 trigger efficiency vs HIP truth pT for the EM Calo barrel (left) and end-cap (right) regions, respectively. The figures show the efficiencies for single HECOs (top) and monopoles (bottom) of mass 1000 GeV for various charges.

1.2

m = 1000 GeV, q = 0.5 gD 0.8 m = 1000 GeV, q = 1.0 gD m = 1000 GeV, q = 1.5 gD m = 1000 GeV, q = 2.0 gD 0.6 Fraction of events passing trigger 0.4

0.2

0 0 500 1000 1500 2000 2500 3000 3500 4000 p [GeV] T

Figure 5.5: EF_g_nocut_hiptrtL2 trigger efficiency with hadronic veto applied offline vs HIP truth pT for the EM Calo barrel. The figure show the efficiencies for single monopoles of mass 1000 GeV for various charges. 5.3. Event Selection 105

The first step of defining the associated TRT region is common for both barrel and end-cap regions. A wedge of width ∆φ = 0.05 rad is ± defined with respect to the φ position of the cluster. Within the wedge, a distribution of the φ positions of all HT TRT hits is built. An average, φavg, is computed with respect to hits in the region of 0.01 rad around ± the peak of this distribution.

1000 900 ATLAS ATLAS

[mm] Simulation [mm] 800 Simulation

TRT 800 TRT Y Y 700 600 600 400 500

200 400

0 •1000 •800 •600 •400 •200 0 •900 •800 •700 •600 •500 •400 X X TRT [mm] TRT [mm]

Figure 5.6: Construction of a preselection road in the TRT barrel as described in Sec. 5.3, for a simulated monopole. The LT TRT hits are shown in green and the HT TRT in black. The blue lines define the ∆φ = 0.05 rad wedge and the black lines are the final 4 mm road. To ± ± the right is a zoomed-in view of the same event as is shown in the left figure.

In the barrels, where the TRT straws are parallel to the beam axis and no z information is available, a road in the x-y plane is then defined as 4 mm with respect to φavg. This is shown in Fig. 5.6. This definition ± is chosen as it encompasses two TRT straws, enough to collect δ-rays, but narrow enough to make the pile-up dependence insignificant. Using the z position of the calorimeter cluster, the TRT region is restricted to one of the two TRT barrels (z > 0 or z < 0), with an exception if η < 0.1, | | where hits from both barrels are counted. In the end caps, the straws are oriented radially, and thus no r position can be retrieved. The region is here a wedge defined by ∆φ = 0.006 rad ± with respect to φavg, as it corresponds to two straws at the inner radius of the end-cap. 106 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

The number of HT and LT TRT hits, NHT,presel and NLT,presel, respectively, are counted in the associated TRT region. The fraction of high threshold hits, fHT,presel, is then calculated and the following requirements are imposed on a preselection candidate:

Calorimeter cluster ET > 16 GeV •

NHT,presel > 9 •

NHT,presel/(NHT,presel + NLT,presel) = fHT,presel > 0.4 • Further Selections After ensuring no candidates share the same TRT region, a set of requirements described in this section are applied to each of the preselection candidates. Finally, in case of multiple candidates in the same event, only one candidate is selected. These requirements are summarised below and described in the text that follows. The quantities Epre (ET,pre) and EEMX (ET,EMX ) represent the (transverse) energy of the calorimeter cluster deposited in the EM Calo presampler and EMX, where X = 1,2,3. The Ehad represents the cluster energy deposited in the hadronic barrel and extended barrel. The variable fHT , which is a reﬁned version of the fHT,presel, mentioned above, will be described in the next section.

Overlap removal: If several clusters are associated to same TRT • region (from the preselection), the cluster with the highest Epre + EEM1 is chosen.

EM Calo cluster transverse energy: ET,pre+ET,EM +ET,EM + • 1 2 ET,EM3 > 16 GeV.

EM Calo layer energies: Epre > 5 GeV or EEM > 5 GeV. • 1 Pseudorapidity: 0 < η < 1.375 or 1.52 < η < 2.0. • | | | |

Oﬄine hadronic veto: Ehad < 1 GeV. • Single candidate: The candidate with the highest fHT value is • kept.

Several clusters could be associated with the same TRT region due to noise or inefficiencies in the cluster algorithm. An overlap removal is applied to select one cluster per TRT region. This has no effect on the 5.3. Event Selection 107 signal efficiency as shown in Figs. 5.7 and 5.8. A transverse energy cut on the calorimeter cluster is applied, since the preselection energy cut was applied to the total energy, including energy in the hadronic calorimeter. A HIP reaching the second EM Calo layer must have traversed the previous layers. To protect against noise and cosmic radiation, the cluster is required to have a considerable energy deposit in either the presampler or the first EM Calo layer. The selection variable, w, described in the next section, is defined with respect to EM Calo cell information. To ensure the reliability of w over the full range of pseudopradity covered here, the EM Calo barrel-end-cap transition region is excluded. The pseudorapidity range is also confined to that of the TRT. As mentioned in Sec. 5.3, an offline hadronic veto is applied, imposing a maximum value of the energy deposition in the hadronic calorimeter. 108 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

m = 1000 GeV, q = 10 e 50000 m = 1000 GeV, q = 20 e m = 1000 GeV, q = 40 e m = 1000 GeV, q = 60 e 40000

Events passing selection 30000

20000

10000

0 Total L1_EM18VHEF_g_nocut_hiptrtL2PreselectionOverlap removalEM Et > 16pre_E GeV OR0 EM1_E < |eta| >= fHTTRT0.94 >= 0.7

Figure 5.7: Event level cut-flow showing event selections for simulated single particle HIPs of mass 1000 GeV and various charges. The first four bins show the effect of the L1 trigger (L1 EMVH18), HIP trigger (EF g nocut hiptrtL2), described in Sec. 5.3 and the preselection, described in Sec. 5.3, where the corresponding bin labels are given in paren- thesis. Bins five to ten show the further selections, explained in Sec. 5.3: Overlap removal, EM Calo cluster transverse energy (EM Et > 16 GeV), EM Calo layer energies (pre E OR EM1 E > 5 GeV), pseudorapdity (0 < η < 1.375 OR 1.53 < η < 2.0), offline hadronic veto (Hadronic veto) | | | | and single candidate (Max fHTTRT cluster). The last two bins correspond to the final discrimination variable selections w 0.94 (w avg >= ≥ 0.94) and fHT 0.7 (fHTTRT >= 0.7) as described in Sec. 5.3. ≥ 5.3. Event Selection 109

m = 1000 GeV, q = 0.5 gD 50000 m = 1000 GeV, q = 1.0 gD m = 1000 GeV, q = 1.5 gD m = 1000 GeV, q = 2.0 gD 40000

Events passing selection 30000

20000

10000

0 Total L1_EM18VHEF_g_nocut_hiptrtL2PreselectionOverlap removalEM Et > 16pre_E GeV OR0 EM1_E < |eta| >= fHTTRT0.94 >= 0.7

Figure 5.8: Event level cut-ﬂow showing event selections for simulated single particle HIPs of mass 1000 GeV and various charges. The bin labels are the same as in Fig. 5.7 and are described in the caption of that ﬁgure. 110 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

Final Selections

The two discriminating variables, fHT and w, represent the characteristic features of the HIP signature: a large fraction of HT TRT hits and a narrow EM Calo cluster, as described in Chap.4. The quantity fHT is a reﬁnement of the fHT,presel variable, taking into account the transition regions in the TRT:

+ − ± If the EM Calo cluster satisﬁes η < 0.1, fHT = max(f , f , f ) • | | HT HT HT where +, and stands for positive z, negative z TRT barrel, or both, − ± respectively.

If the EM Calo cluster satisfies 0.77 < η < 1.37, • B EC B+EC | | fHT = max(fHT , fHT , fHT ) where B and EC stand for TRT barrel and endcap. The wi variables, where i = presampler, EM1 or EM2, are the fractions of energy in the 2 (presampler), 4 (EM1) or 5 (EM2) most energetic cells of the EM Calo cluster. The difference in the numbers of most energetic cells between the different layers is a consequence of the differing granularity of the EM Calo layers. The w variable is an average of the layer-specific variables, where only layers with a considerate energy deposition is included in the average to avoid including noise:

1 P w = (wi), for all i = presampler, EM1, EM2 for which the • n P energy of that layer, Ei > 5 GeV, and n = i.

In Fig. 5.9, DY HIP distributions of fHT are shown for several signal samples and simulated background samples (see Sec. 5.2) together with collision data. The fHT variable is very sensitive to the HIP charge, resulting in considerable signal contamination in control region C, (see Sec. 5.7) defined as w > 0.94, fHT < 0.7, for charges 20 e or 0.5 gD. ≤ ≤ The signal leakage in percentages for all samples are given in Tab. 5.2. Example w distributions for DY HIPs are shown in Fig. 5.10 together with data and simulated background. In general, the w variable has a very good discrimination power. A degradation of the w variable is observed as a consequence of the bending in the magnetic field or showering δ-rays for some samples resulting in signal contamination into control region B (w < 0.94, fHT 0.7) as can be seen in Tab. 5.2. As expected, low mass ≥ and high charge correlate with the signal leakage into B. It can also seen that monopoles are more affected than HECOs, which is due to the fact 5.3. Event Selection 111

m=1000 GeV, q=10e m=500 GeV, g=0.5g a.u. 0.35 a.u. 0.35 D m=1000 GeV, q=20e m=500 GeV, g=1.0g D m=1000 GeV, q=40e m=500 GeV, g=1.5g D 0.3 m=1000 GeV, q=60e 0.3 m=500 GeV, g=2.0g D High•p di•jets High•p di•jets T T 0.25 DY → ee 0.25 DY → ee W± → νe± W± → νe± 0.2 Data 2012 • s = 8 TeV (7.0 fb •1) 0.2 Data 2012 • s = 8 TeV (7.0 fb •1)

0.15 0.15

0.1 0.1

0.05 0.05

0 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

fHT fHT

Figure 5.9: Distributions of the fHT variable for a set of simulated DY HECOs of mass 1000 GeV (left) and DY monopoles of mass 500 GeV (right) of various charges, together with simulated background and data. On both data and the MC predictions, trigger, preselection and the further selections were imposed. For data, the signal region was blinded.

m=1000 GeV, q=10e

a.u. a.u. m=500 GeV, g=0.5g D 0.5 m=1000 GeV, q=20e 0.5 m=500 GeV, g=1.0g m=1000 GeV, q=40e D m=500 GeV, g=1.5g m=1000 GeV, q=60e D High•p di•jets High•p di•jets T 0.4 T 0.4 → DY → ee DY ee ± ± W± → νe± W → νe 0.3 Data 2012 • s = 8 TeV (7.0 fb •1) 0.3 Data 2012 • s = 8 TeV (7.0 fb •1)

0.2 0.2

0.1 0.1

0 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 W W

Figure 5.10: Distributions of the w variable for a set of simulated DY HECOs of mass 1000 GeV (left) and DY monopoles of mass 500 GeV (right) of various charges, together with simulated background and data. On both data and the MC predictions, trigger, preselection and the further selections were imposed. For data, the signal region was blinded. 112 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS that the monopole bending is in the η direction, where the granularity of the EM Calo is finer in the presampler and EM1 compared to φ, in which the HECOs are deflected. In addition, lower mass HIPs of high kinetic energy can produce δ-rays (see Sec. 4.3) with an energy in the Bremsstrahlung regime in the EM Calo, possibly causing cascades. The fHT and w variables show robustness to pile-up for all signal samples. Events with at least one candidate fulfilling the following requirements are selected:

w 0.94 • ≥

fHT 0.7 • ≥

The selection thresholds were determined by optimising s/√s + bg, where s stands for simulated signal yield and bg for the background yield.

Sample b c d 0.5 g Sample b c d D 200 GeV 1.6 2.3 0 10.0 e 500 GeV 1.2 4.3 0 200 GeV - - - 1000 GeV 0.6 20 0.1 500 GeV - - - 1500 GeV - - - 1000 GeV - - - 2000 GeV - - - 1500 GeV - - - 2500 GeV - - - 2000 GeV - - - 1500 GeV 0.3 27 0 2500 GeV - - - 2000 GeV 0.5 31 0 20.0 e 2500 GeV 0.8 26 0.2 200 GeV 1.2 48 0.3 1.0 g 500 GeV 0.6 36 0.2 D 200 GeV 8.9 3.3 0.1 1000 GeV 0.4 35 0.2 500 GeV 0.7 1.6 0 1500 GeV 0.2 37 0.1 1000 GeV 0.2 0.8 0 2000 GeV 0.2 37 0.2 1500 GeV 0.1 0.9 0 2500 GeV 0.5 36 0.1 2000 GeV 0.1 1.4 0 40.0 e 2500 GeV 0.1 1.9 0 200 GeV 0.4 4.3 0.0 1.5 g 500 GeV 0.1 1.5 0.0 D 200 GeV 8.0 2.6 0.1 1000 GeV 0.1 1.0 0.0 500 GeV 0.5 1.6 0 1500 GeV 0.1 0.9 0.0 1000 GeV 0.1 0.9 0 2000 GeV 0.0 1.3 0.0 1500 GeV 0.1 0.6 0 2500 GeV 0.0 1.6 0.0 2000 GeV 0.1 0.7 0 60.0 e 2500 GeV 0.1 0.7 0 200 GeV 2.4 3.6 0.0 2.0 g 500 GeV 0.3 2.1 0.0 D 200 GeV 19 1.4 0.2 1000 GeV 0.1 1.1 0.0 500 GeV 0.4 1.6 0.0 1500 GeV 0.1 1.0 0.0 1000 GeV 0.1 0.6 0.0 2000 GeV 0.1 0.8 0.0 1500 GeV 0.1 0.3 0.0 2500 GeV 0.1 0.6 0.0 2000 GeV 0.1 0.4 0.0 2500 GeV 0.0 0.5 0.0

Table 5.2: Leakages (a, b, c and d) of the signal into the background control regions B D in percentages, for single HECOs (left) and single − monopoles (right). 5.4. Single Particle Selection Eﬃciency and Fiducial Regions 113

5.4 Single Particle Selection Eﬃciency and Fiducial Regions

As discussed in Sec. 1.3, predictions of HIP production models are limited by the non-perturbative nature of the HIP coupling to the photon. Single particle samples are used to determine kinematic regions where the search presented here has high and uniform sensitivity, called fiducial regions, and limits are estimated with respect to these regions. These limits are model-independent in the sense that no specific production model was assumed, and are intended to be combined with any model of which the kinematic distributions can be calculated. Comparing the number of expected number of events of that model in the fiducial regions to the corresponding limit, the extent to which this model is already probed by this search can be inferred. The L1 trigger acceptance is the dominating contribution to the overall selection acceptance, as is discussed in Sec. 5.3. This is also clearly visible in the cut-flows in Figs. 5.7 and 5.8. A HIP will be undetected if it stops before the EM Calo and thus not fire the L1 trigger, or if it reaches the hadronic calorimeter and fires the L1 hadronic veto. In addition, the energy deposition in the EM Calo has to ensure a cluster ET of at least 18 GeV. The HIP ionisation energy loss per unit of length is governed by its charge and speed as well as by the properties of the detector material, see Chap.4. For a HIP with a given mass and charge, the factors determining if it will be within the acceptance or not are therefore the initial kinetic energy and the amount and type of material traversed. Maps of kinetic energy vs pseudorapidity were therefore used to define fiducial regions, separately for each mass and charge point. The large number of mass and charge points and the complexity of the problem of finding a fiducial region for each of these motivate the need for an algorithm with a simple approach that could be used for all points. Fiducial regions are sought in the EM Calo barrel ( η < 1.475) and | | the EM Calo end-cap (1.375 < η < 3.2) separately. The barrel-endcap | | cryostat transition region (1.375 < η < 1.52) as well as the region outside | | the TRT coverage ( η > 2.0) are also excluded. Due to the truncation of | | the generated initial energy, a sinus shaped edge is present on efficiency maps to the right (left) of which no events were generated. Moreover, there is a noticeable efficiency drop in the TRT barrel-endcap transition region (0.63 < η < 1.06) most visible for the lower HIP charges. As a | | result, two separate pseudorapidity ranges are considered when searching 114 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS for fiducial regions in the EM Calo barrel region. The three pseudorapidity ranges are in this text referred to as Aη (0 < η < 1.0), Bη | | (1.0 < η < 1.375) and Cη (1.52 < η < 2.0). The separation into three | | | | ranges was a compromise between keeping the algorithm simple, i.e. not introducing more complicated fiducial region shapes, and not omitting too much of the high efficiency region. The bin size used is 25 GeV in kinetic energy and 0.05 in pseudorapidity. The complexity is to a large extent reduced if the shapes of the fiducial regions can be constrained to rectangles. By taking into account how the material in the detector is oriented (along z axis in the barrel and in x- y-plane in the endcaps), the kinetic energy observable could be modified to account for the angle dependence of the penetration power. The ηmin and ηmax define the start and end of the fiducial region | | | | in η and Ekin and Ekin give the start and end of the region in terms | | min max of kinetic energy, Ekin. The algorithm identifies the rectangle with the kin kin largest area, where the area is defined as 2 ( ηmax ηmin ) (E E ), · | |−| | · max− min fulfilling the following properties:

1 PN avg > min, where avg = i and i is the eﬃciency of bin i. • N i=1 The sum goes over all N bins in the rectangle.

min = 0.9. ◦ σ < σ , where σ is the standard deviation of the average eﬃ- • max q 1 PN 2 ciency deﬁned as σ = (i avg) . N i=1 − σ = 0.12. ◦ max

The values of min and σmax , representing the requirements on minimum average efficiency and maximum standard deviation of the efficiency over the fiducial region, respectively, were chosen taking into account the performance of the algorithm for all samples. As the efficiency in the centre of a high efficiency region is > 95%, the choice of min mostly affects the edges of the region, where irregularities preventing a region from having perfect rectangular shape can be accounted for by allowing some lower efficiency bins. The σmax was introduced to be able to quantify this deviation and protect against too large deviations. Occasionally, there are bins with no event information.2 A fiducial region containing two or more such bins adjacent to each other, is not considered by the algorithm, since

2The bin size was set as a compromise between gaining knowledge of the distribution’s shape and having good statistical precision in the bin contents. 5.4. Single Particle Selection Efficiency and Fiducial Regions 115 it is regarded as resulting in a too large uncertainty. This also protects against including part of the phase space to the right of the “truncation edge”. A single bin without any information surrounded by bins with information is however allowed and its efficiency value is taken as the average of those of the surrounding bins. The algorithm is divided into two intermediate steps, “Step I” and “Step II”, outlaid below, and they consider each of the three η-ranges separately. Step II is the part of the algorithm that by far requires the most computing resources. The functionality of Step I is to reduce the region that Step II has to operate on. This greatly greatly reduces the overall computing time of the algorithm. kin The outcome of Step I is a so called start region, defined as Emin,SR < kin Ekin < Emax,SR in terms of kinetic energy, and where SR represents start region. Step I does not constraint the pseudorapidity range, and the start region will therefore have the full η-range of Aη, Bη or Cη.

Step I: A ﬁrst estimate of the interval of high eﬃciency in kinetic energy

1. For all η bins, in increasing order of η, starting at the lowest value of η, the following procedure is applied:

1 a) Scan all Ekin bins in increasing order of Ekin, starting from the bin corresponding to Ekin = 0 (η bin is ﬁxed).

– If i min for 3 consecutive bins (75 GeV), save the Ekin ≥ kin value corresponding to the ﬁrst of these bins as Emin,η, where η is the pseudorapidity value of the current bin. – Otherwise, repeat the above process on the next η bin.

kin kin 2. Take the smallest Emin,η found as Emin,SR. 3. For all η bins, in increasing order of η, starting at the lowest value of η, the following procedure is applied:

3 a) Scan all Ekin bins in decreasing order of Ekin starting from the bin corresponding to Ekin = 3500 (η bin is ﬁxed).

– If i min for 3 consecutive bins, (75 GeV), save the Ekin ≥ kin value corresponding to the ﬁrst of these bins as Emax,η, where η is the pseudorapidity value of the current bin. – Otherwise, repeat the above process on the next η bin. 116 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

kin kin 4. Take the largest Emax,η found as Emax,SR.

Step II: Finding the largest rectangle with avg > min and σ <

σmax 1. For all possible rectangles within the start region in order of decreasing area. (Regions with equal area are ordered in terms of increasing kin Emin,SR):

1 a) Calculate the avg and σ

– If avg > min and σ < σmax , the ﬁducial region is found. Otherwise, continue.

The algorithm computing time of Step II 1 a) is greatly reduced by reusing information from the start region, which then is the only region for which the average efficiency has to be calculated explicitly. For each of the regions considered in Step II 1, to obtain the average efficiency of the region, information about the number of bins and the total sum of their contents are extracted only from the residual regions with respect to the start region and then subtracted from the corresponding quantities for the start region. Examples of fiducial regions for monopoles of mass 1000 GeV and charge 1.0 gD and HECOs of mass 1000 GeV and charge 40 e are presented in Fig. 5.11. The complete set of regions are listed in Tabs. 5.8- 5.11. The size and position of the fiducial regions vary between different samples. In general, the kinetic energy value where the acceptance region starts represents the minimum kinetic energy needed to reach the EM Calo, while the upper kinetic energy threshold is due to the hadronic veto of the L1 trigger. As can be seen in Fig. 5.11, both the minimum and maximum Ekin for a fiducial region increase with charge, q, as the HIP ionisation is proportional to q2. A high ionisation results in a larger probability of stopping before reaching the EM Calo or the hadronic calorimeter. In Tabs. 5.8- 5.11 a mass dependence of the efficiency can also be seen. For HECOs, a larger mass means lower speed and more ionisation and both the minimum and maximum Ekin increases with mass. For monopoles, the ionisation energy loss increases with speed. The acceptance is more complicated and the mass dependence varies more with the charge. For high kinetic energy, the resulting high speed which contributes to a high ionisation competes with the fact that a high kinetic energy allows it to penetrate further into the detector. The kinetic energy 5.4. Single Particle Selection Efficiency and Fiducial Regions 117 threshold required to reach the EM Calo possibly represents the point where the penetration power effect gets more important than the high ionisation. For the high charges of 1.5 gD and 2.0 gD, the minimum Ekin decreases with increasing mass as the speed decreases and the point where the penetration power is more important is reached earlier. The kinetic energy threshold for reaching the hadronic calorimeter is for these charges in general larger than the maximum generated kinetic energy and the maximum Ekin value given in Tab. 5.11 do not represent this value, but depend more on the shape of the acceptance at low Ekin values. For charges 1.0 gD and 0.5 gD, the threshold for reaching the EM Calo is less dependent on mass. The deviations seen in Tab. 5.10 are due to differences in the acceptance close to the transition regions. On the other hand, a mass dependence can be seen for the maximum Ekin value for a fiducial region, which here represents the kinetic energy required to reach the hadronic calorimeter. When no fiducial region of high efficiency is found for a given mass and charge, no model-independent cross-section limit can be determined for that sample. This is the case for several mass and charge points where the acceptance in general is very low, for example for HIPs with low charges since these might not ionise enough to fire the L1 trigger where 18 GeV EM Calo energy deposition is required, even though they do reach the EM Calo. The kinetic energy threshold for reaching the hadronic calorimeter and firing the hadronic veto is also very low, resulting in a minimal region in kinetic energy between reaching the EM Calo and reaching the hadronic calorimeter. No fiducial region of high efficiency was found for HECOs of charge 10 e, nor for monopoles of charge 0.5 gD and mass 1500 GeV 2500 GeV. For monopoles of charge 0.5 gD and − mass 500 GeV and 1000 GeV, regions of high efficiency were found in the Bη only, and Bη and Cη ranges only, respectively. This difference between low and high masses monopoles is possibly due to the reversed ionisation energy loss dependence on velocity for monopoles, as discussed above. HECOs of charge 20 e also have low sensitivity, as can be seen in Fig. 5.11, and in Bη and Cη, no fiducial regions are found. With a very high ionisation energy loss, the HIP may stop before reaching the EM Calo in the whole kinetic energy range considered. For monopoles of charge 2.0 gD and mass 200 GeV, no region is found for Cη. 118 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

3500 1 3500 1 0.9 0.9 3000 m = 1000 GeV, q = 20 e 3000 m = 1000 GeV, q = 20 e [GeV] 0.8 [GeV] 0.8 kin L 2500 kin L 2500 E 0.7 E 0.7

2000 0.6 2000 0.6 0.5 0.5 1500 0.4 1500 0.4 1000 0.3 1000 0.3 0.2 0.2 500 500 0.1 0.1 0 0 0 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 η η

3500 1 3500 1 0.9 0.9 3000 m = 1000 GeV, q = 40 e 3000 m = 1000 GeV, q = 40 e [GeV] 0.8 [GeV] 0.8 kin T 2500 kin L 2500 E 0.7 E 0.7

2000 0.6 2000 0.6 0.5 0.5 1500 0.4 1500 0.4 1000 0.3 1000 0.3 0.2 0.2 500 500 0.1 0.1 0 0 0 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 η η

3500 1 3500 1 0.9 0.9 3000 m = 1000 GeV, q = 60 e 3000 m = 1000 GeV, q = 60 e [GeV] 0.8 [GeV] 0.8 kin T 2500 kin L 2500 E 0.7 E 0.7

2000 0.6 2000 0.6 0.5 0.5 1500 0.4 1500 0.4 1000 0.3 1000 0.3 0.2 0.2 500 500 0.1 0.1 0 0 0 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 η η

3500 1 3500 1 0.9 0.9 3000 m = 1000 GeV, q = 1.0 gD 3000 m = 1000 GeV, q = 1.0 gD [GeV] 0.8 [GeV] 0.8 kin T 2500 kin L 2500 E 0.7 E 0.7

2000 0.6 2000 0.6 0.5 0.5 1500 0.4 1500 0.4 1000 0.3 1000 0.3 0.2 0.2 500 500 0.1 0.1 0 0 0 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 η η

Figure 5.11: Examples of fiducial regions in the barrel (left) and end caps (right) regions found by the algorithm described in Sec. 5.4 imposed on analysis selection efficiency maps of initial kinetic energy and pseudorapidity. The top six figures show efficiencies for simulated HECOs of mass 1000 GeV and various charges, and the bottom two show efficiencies for monopoles of mass 1000 GeV and charge 1.0 gD. The y-axis title abbreviations stand for Ekin sin θ and Ekin cos θ, respectively. A white bin corresponds to either no information or zero efficiency. 5.5. Drell-Yan Signal Selection Efficiency 119

Selection Candidates Rel. Events Rel. efficiency efficiency All — — 20000 — L1_EM18VH — — 6319 0.32 EF_g_nocut_hiptrtL2 — — 4481 0.71 Preselection 6487 — 4432 0.99 Overlap removal 6262 0.97 4432 1.0 EM Calo cluster transverse energy 6244 1.0 4431 1.0 EM Calo layer energies 6230 1.0 4421 1.0 Pseudorapdity 5800 0.93 4072 0.92 Offline hadronic veto 5782 1.00 4071 1.00 Single candidate 4071 0.7 4071 1.00 w ≥ 0.94 4065 1.00 4065 1.00 fHT ≥ 0.7 4018 0.99 4018 0.99

Table 5.3: Candidate (event) cut-flow for simulated DY HECOs of mass 1000 GeV and charge 40 e. The selections are defined in the text. The relative efficiency gives the fraction of candidates (events) passing the selection out of those passing the previous selection.

5.5 Drell-Yan Signal Selection Eﬃciency

The kinetic energy distributions for DY HIPs peak at low values, see Fig. 5.3. In general, the acceptance is therefore low and very model dependent, since it is based on low statistical precision in the tails of the kinetic energy distribution. This is especially pronounced for high charges for which the kinetic energy required to reach the EM Calo is high, as discussed in the previous section. The acceptance correlates negatively with charge, with the exception of 10 e and 0.5 gD, for which the acceptance is very low in general. For HECOs a higher mass means that higher kinetic energy is required for high acceptance, and the efficiency generally decreases with mass. For monopoles, lower masses also have lower efficiency as the higher speed means more ionisation. DY models with an acceptance < 1% are excluded from this search. The excluded models are all monopoles with charge 2.0 gD as well as those with charge 1.5 gD and mass 200 GeV and HECOs of charge 60 e and mass 2500 GeV. Example event and candidate cut-flows are given in Tabs. 5.3- 5.4. The tables show that, as for the single particles, the L1_EM18VH trigger has the lowest signal efficiency, followed by the EF_g_nocut_hiptrtL2 trigger. The other event selections have high signal efficiency ( 99%) ≤ with the exception of the pseudorapdity cut. 120 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

Selection Candidates Rel. Events Rel. efficiency efficiency All — — 20000 — L1_EM18VH — — 7962 0.4 EF_g_nocut_hiptrtL2 — — 6526 0.82 Preselection 11253 — 6503 1.00 Overlap removal 10877 0.97 6503 1.0 EM Calo cluster transverse energy 10794 0.99 6503 1.0 EM Calo layer energies 10787 1.00 6503 1.0 Pseudorapdity 10310 0.96 6242 0.96 Offline hadronic veto 10286 1.00 6242 1.0 Single candidate 6242 0.61 6242 1.0 w ≥ 0.94 6224 1.00 6224 1.0 fHT ≥ 0.7 6195 1.00 6195 1.0

Table 5.4: Candidate (event) cut-flow for simulated DY monopoles of mass 1000 GeV and charge 1.0 gD. The selections are defined in the text. The relative efficiency gives the fraction of candidates (events) passing the selection out of those passing the previous selection.

5.6 Systematic Uncertainties

Sources of systematic uncertainties affecting the signal efficiency have been identified and estimated. The uncertainty on the luminosity was obtained from Ref. [155]. The other systematic uncertainties have been calculated using two different procedures. Some have been estimimated using dedicated samples in which simulation parameters relating to HIP detector interaction have been modified. These samples each contain 5000 events. The systematic uncertainties are obtained from comparing the efficiency for nominal samples to those modified to model the effect of the systematic uncertainty source, and are expressed as relative uncertainties with respect to to the nominal efficiencies. They are estimated for each sample separately. The other systematic uncertainties were estimated using the SP (50 000 events) and DY (20 000) samples with nominal simulation settings. For these, the effects of the systematic uncertainty could be estimated by making modifications to the data analysis. For each of the different sources, the uncertainty is averaged over all particles with the same charge, since no mass dependence was seen and differences between them are regarded as of statistical nature. The systematic uncertainties for single particles, used when setting fiducial limits, were estimated using events within the fiducial regions only. All systematic uncertainties are regarded as independent and added in quadrature. 5.6. Systematic Uncertainties 121

Charge MC Det. G4 Birks’ Birks’ Stat. material range cut high low 20 e 3.9 13 10 6.7 15 ± ± − − − 40 e 0.44 0.08 +0.02 0.27 +0.01 ± ± − 60 e 0.25 0.07 +0.18 +0.36 0.10 ± ± − Charge δ ray TRT EM Calo Total Total − occ. cross-talk (UP) (DOWN) 20 e 0.35 +6.4 1.6 +15 24 ± − − 40 e 0.35 +0.74 0.87 +3 3 ± − − 60 e 0.06 +0.62 2.3 +3 4 ± − − Table 5.5: Relative uncertainties on the signal eﬃciencies in percentages for single HECOs in ﬁducial regions. The total relative uncertainties are calculated as quadratic sums of the individual relative uncertainties including the 2.8% uncertainty on the luminosity measurement. Note that the δ-ray and material density uncertainties are taken as symmetric.

The systematic uncertainties for single particles are given in Tabs. 5.5 and 5.6, for HECOs and monopoles, respectively.

TRT occupancy: The accuracy of the pileup description aﬀects the TRT occupancy, which is important for the fHT variable. The simulated TRT occupancy is underestimated for low values of reconstructed vertices while it is overestimated for high values. This was corrected for at analysis level using the ratio of number of LT TRT between MC and data.

Cross-talk in the EM Calo: Cross-talk, referring to a set of different noises induced by neighbouring cells in the EM Calo, can affect the cluster width important for the w variable. All of the different cross- talk sources are already accounted for in the simulations, except for the inductive cross-talk in φ which was required to be implemented on analysis level.

Detector material density: As explained in Sec. 5.4, the properties of the detector material play a major role in determining the eﬃciency. To estimate the uncertainty in the description of the material in the simulations, a diﬀerent material model to the one used in the analysis was used, the ATLAS-GEO-21-06-01, with 5 15% increase − in the material in the ID. 122 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

Charge MC Det. G4 Birks’ Birks’ Stat. material range cut high low

0.5 gD 1.9 3.6 1.2 1.2 0.27 ± ± − − − 1.0 gD 0.29 0.43 +0.42 +0.52 +0.11 ± ± 1.5 gD 0.23 0.24 +0.27 +0.42 0.02 ± ± − 2.0 gD 0.43 0.85 0.36 +0.32 0.78 ± ± − − Charge δ ray TRT EM Calo Total Total − occ. cross-talk (UP) (DOWN)

0.5 gD 0.35 +1.37 1.58 +5 5 ± − − 1.0 gD 0.06 +0.67 3.2 +3 4 ± − − 1.5 gD 0.33 +0.53 2.6 +3 4 ± − − 2.0 gD 0.27 +0.46 4.2 +3 5 ± − − Table 5.6: Relative uncertainties on the signal eﬃciencies in percentages for single monopoles in ﬁducial regions. The total relative uncertainties are calculated as quadratic sums of the individual relative uncertainties including the 2.8% uncertainty on the luminosity measurement.

Correction to Birk’s law: Birk’s law and the correction to it are described in Sec. 4.2. Uncertainties in the experimental heavy ion data limit the precision of this correction. The correction was varied according to Fig. 4.3.

Delta-ray production model: As explained in Sec. 4.3, δ-rays represent up to 30% of the energy deposition of HIPs. High energy ∼ δ-rays could possibly also cascade in the EM Calo, widening the EM Calo cluster, affecting the w variable efficiency. They can also affect the distribution of the fHT variable. The geant4 model has a 3% associated uncertainty on δ-ray production. The uncertainty was estimated by suppressing the production by this amount. The systematic uncertainties for HECOs were estimated using the monopole uncertainties: 0.5 gD for HECOs of charge of 10, 20 and 40 e and 1.0 gD for 60 e. geant4 range cut: When the δ-electrons are simulated, the displacement that the δ-electron is estimated to cover in the interval between two “time steps” in the simulation is calculated. If this estimated displacement is below a certain value, referred to as the range cut, 5.7. Background Estimation 123

the δ-electrons are not propagated explicitly, and their energy deposition is instead added to the energy of the HIP. As for the δ-ray production model, the range cut can aﬀect the w variable and the fHT variables. The range cut was decreased from 50 µm to 25 µm in the ID.

Luminosity: The uncertainty in to the luminosity measurement is obtained from a calibration of the luminosity scale derived from beam- separation scans performed in November 2012 and is 2.8% [155].

The δ-ray systematic uncertainty is very small, less than 0.5%, for ± HIPs of all charges. The TRT occupancy and G4 range cut systematic uncertainties are also small, less than 1.5% for all charges except for ± the HECO of the lowest charge, 20 e, for which the fHT variable has less discrimination power and thus the 20 e HECO is more sensitive to these systematic uncertainties. The systematic uncertainties due to the correction to Birks’ law are small, less than 1.5% for all HIPs except for ± the 20 e HECOs. The detector material density systematic uncertainty is less than 1% for all HIPs except for the 20 e and 0.5 gD HIPs. The systematic uncertainty due to EM cross-talk is on the order of a few percent for all HIPs. In general, the eﬃciency for the lowest charges is low as discussed in Sec. 5.4. They are thus in general more sensitive to the systematic uncertainties.

5.7 Background Estimation

In the absence of simulated background samples that fully model the SM background, a purely data driven approach called the ABCD method is employed. The ABCD method exploits three control regions, referred to as regions B, C and D, to estimate the background yield in the signal region, referred to as region A. The regions are defined with respect to a plane of two observables, as can be seen in Fig. 5.12, and the method relies on the two observables being largely uncorrelated for the background population. The event yield for the background in the different regions, NA,NB,NC and ND are then related as NA/NB = NC /ND. The final selection observables, w and fHT , are sufficiently independent, meaning that their slight correlation can be modelled within the ABCD method, to be used as the ABCD variables defining the signal 124 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS and control regions. The correlation and the modelling of it will be explained below. As discussed in Sec. 5.3 there are for some samples considerable signal contamination into the control regions. A more sophisticated ABCD method using a likelihood is therefore used to make model- dependent background estimates, taking the correlation, signal leakage and also the systematic uncertainty of the signal efficiency for each model separately into account. The likelihood is also integrated into the limit- setting procedure, which is discussed in Sec. 5.8. As a cross-check, the simple ABCD method background estimate was calculated:

nBnC nA,est = = 0.41 0.24(stat.) (5.1) nD ±

where nB, nC and nD are the observed number of events in the B, C and D regions given in Tab. 5.7. The parameter nA,est is the estimated background yield in the signal region A.

Deﬁnition of Regions and Data Yield

Figure 5.12: Distribution of the discriminating variables fHT and w for 2012 data (“rainbow colours”) and simulated DY monopole of mass 1000 GeV charge gD (black dots). In the ﬁgure, the deﬁnition of the regions A, B, C and D are superimposed as red lines and green labels.

The control and signal regions are deﬁned as follows: 5.7. Background Estimation 125

A: (signal region) fHT 0.7, w 0.94 ≥ ≥ B: (control region) fHT 0.7, 0.83 < w < 0.94 ≥ C: (control region) fHT < 0.7, w 0.94 ≥ D: (control region) fHT < 0.7, 0.83 < w < 0.94 The number of observed events are given in Tab. 5.7 and in Fig. 5.12 the definition of the regions is given graphically. As can be seen in this figure, the bulk of the data is populating the B and D regions. The significant differences in statistical precision in the different control regions is problematic when using a likelihood method, since the background estimation will be much more sensitive to a variation in τB than in τC . This introduces a correlation between these two parameters, as discussed below. The B and D regions were reduced to the region close to the control region, starting from w = 0.83, to make this difference less significant.

Region: A B C D Number of observed events: 0 618 3 4539

Table 5.7: The observed number of events in the signal region (A) and the control regions (B, C and D).

Likelihood A likelihood, , is constructed assuming Poisson distributed event yields L in each of the regions A, B, C and D:

−µi ni U Y e µi = P (nA, nB, nC , nD µ, µ , τB, τC ) = . (5.2) L | ni! i=A,B,C,D where nA, nB, nC and nD are the observed events in each of the regions, and Eq. 5.2 gives the probability of the observed data given the param- U eters µ, µ , τB and τC . The parameters µi, the averages of the Poisson U distributions for each of the regions i, are modelled in terms of µ, µ , τB and τC as follows: U µA = sig µ + µ , · U µB = sig bµ + µ τB, · U µC = sig cµ + µ τC , · U µD = sig dµ + µ τBτC κ (5.3) · · 126 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

The parameter of interest, µ, represents the number of signal events in the signal region A. The nuisance parameter µU represents the number of background events in this region. The constants b d give the signal − contamination and are expressed as the ratio of expected signal in any of the regions B-D, to that in the signal region A. The signal contaminations are given in Tab. 5.2 for each mass-charge signal point separately. Parameters τi, where i = B,C,D, denote the ratios of the number of background events, µi,bg, in the control regions i, to the parameter U µ , the number of background events in the signal region A. The τi U U parameters thus fulﬁll τi = µi,bg/µ . Using µ /µC,bg = µB,bg/µD,bg, the τD parameter can be expressed in terms of τB and τC :

U τD = µD,bg/µ U U τBτC = (µB,bg/µ ) (µC,bg/µ ) · U U = (µD,bg/µC,bg) (µC,bg/µ ) = µD,bg/µ = τD (5.4) ·

The systematic uncertainties on the signal efficiency is represented by sig. The modelling of the systematic uncertainties is described in more detail below. The possible correlation between the discriminating variables used in the ABCD method is taken into account in the likelihood as a correction to the assumption that the yields in the different regions re- U late as µ /µC,bg = µB,bg/µD,bg by introducing a correction, κ, where U · µ /µC,bg = κ µB,bg/µD,bg. This correction, κ, is modelled in the likeli- · hood as a constant factor of κ = 0.6, κ = 1 or κ = 1.4 in the D region U Poisson factor, where the background yield is given by µ τBτC κ. The · different values of κ will be discussed below. U 3 Finally, the µ, µ , τB, τC , sig are free fit parameters, which are determined by maximising the likelihood function Eq. 5.2 with respect to to the observed events given in Tab. 5.7.

Correlation of Discrimination Variables

The fHT and w show a slight correlation which is geometrical in origin. The w variable is sensitive to the granularity of the EM Calo, which is diﬀerent for diﬀerent pseudorapidity ranges. The fHT is sensitive to ionisation energy loss, which in turn depends on the speed of the HIP,

3The fits are performed within a range in the parameter space, sufficiently large so as not to to introduce a bias in the fit result. 5.7. Background Estimation 127 which is affected by the amount of material passed before reaching the TRT. To evaluate the impact of the correlation on the background estimate and correct for it, the κ parameter, defined above, is introduced. The statistical precision of the data close to the signal region is low and in the absence of background MC samples, the correlation in and close the signal region can only be approximated. Therefore, a range of possible values of κ is estimated and taken into account in the limit-setting procedure. In Fig. 5.13, possible values of κ are presented. For each specific w bin (indexed i), nBi /nDi is computed, where nBi (nDi ) is the observed number of events in region B (D) within the w interval corresponding to bin i. The nBj /nDj in any other w bin with a higher w (indexed j), could be regarded as a possible nA/nC value. By comparing the numbers in all w bins to the right of any specific w bin, correlation corrections κi,j are n /n Aj Cj obtained: κi,j = . The correction factor for a given w bin, κi, is nB /nD i i P Wi,j κi,j a weighted average over all κi,j: κi = P where the sum goes over Wi,j 1 all bins j and Wi,j = 2 i.e. the weight is the reciprocal of the sta- (σκi,j ) tistical uncertainty on κi,j. The average over all κi is very close to 1 and the maximum deviation from 1 is of the order of 40%, as can be seen by inspecting inspecting Fig. 5.13. The value and variation of κ = 1.0 0.4 ± is regarded to constitute a good envelope for the possible ranges of κ.

Modelling of Systematic Uncertainties

The systematic uncertainty sig represents the eﬀect of systematic uncertainties on the signal eﬃciency, as described in Sec. 5.6. The sig is in turn modelled as a function of the source of systematic, αs, such that:

sig = sig(αs) (5.5)

+ The sig parameter has values sig = 1 for αs = 0, sig = sig for αs = 1 − + − and sig = for αs = 1, where the ( ) correspond to the sig − sig sig estimated total positive (negative) systematic effects on the efficiency for all samples separately, as given in Tabs. 5.5 and 5.6. Note that the source, αs, is in this case not directly interpretable as a the very physical source of the variation, since there are several sources, the effect on the efficiency of which are added in quadrature to obtain the total positive and a total negative effect. Piecewise exponential 128 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

c 4

3.5 s = 8 TeV L dt = 7.0 fb•1 3 ∫ 2012 Data 2.5

1.5

0.5

0 0.7 0.75 0.8 0.85 0.9 0.95 w

Figure 5.13: Possible values of correlation correction factor κ (here denoted as “c”). The value of κ in a given w bin i is denoted κi is computed as the weighted average of all possible κi,j for j bins above i, as described in the text.

interpolation as described in Ref. [156], is used to model the function + − Eq. 5.5 between and beyond sig (sig). A constraint factor, C(a αs), is added to the likelihood Eq. 5.2 | which now becomes:

−µi ni Y e µi = C(a αs) (5.6) L ni! · | i=A,B,C,D where a is a so called auxiliary measurement, denoting the nominal value for αs, and the function C(a αs) is assumed to be Gaussian, G(a αs, 1). | | In this search, the αs parameter represents the signal efficiency and the value of a is the measured value of the signal efficiency. In this case, this nominal efficiency is normalized to sig = 1, giving a = 0, and the observed value of the signal efficiency is then combined with the limit on the number of events in calculating the limit on the cross section The αs is a likelihood parameter and the µi depend on αs, according to Eq. 5.3. It is thus allowed to float when the likelihood is maximised. The C term in Eq. 5.6 this way constrains the possibles fit value of the systematic uncertainties, represented by αs. 5.8. Statistical Procedure for Limit Setting 129

5.8 Statistical Procedure for Limit Setting

The CLs Method

The CLs method [157] is a frequentist statistical procedure for setting exclusion limits. Using a profile likelihood test statistic,q ˜µ, described in more detail below, the observed p-value is calculated for a specific signal strength µ and is referred to as pµ: Z ∞ pµ = f(˜qµ)dq˜µ (5.7) q˜µ,obs where f is the distribution ofq ˜µ for the signal + background assumption obtained from pseudo experiments with both signal and background events, andq ˜µ,obs is the test statistic value for observed data. The p-value for the background only hypothesis, p0, is then calculated in the same way from pseudo experiments where zero signal strength is 0 assumed, that is with µ = 0. One then defines a ratio, pµ, of the p-values as:

0 pµ pµ = (5.8) p0

This procedure is repeated with increasing signal strength until a µ = µup 0 satisfying pµup = 5% is reached. The upper limit on the signal strength µ is taken as µup. This way of putting a limit on the ratio of the power and the size of the test, is by construction protecting against putting a too conservative limit in case of possible downwards ﬂuctuations of the data.

The Test Statistic

The CLs method test statisticq ˜µ [158] is based on the likelihood ratio λ˜(µ), deﬁned as:

ˆ  L(µ,θˆ(µ))  ˆ ifµ ˆ 0,  L(ˆµ,θ) ≥ λ˜(µ) = (5.9)  ˆ  L(µ,θˆ(µ))  ˆ ifµ ˆ < 0 L(0,θˆ(0)) where L(µ, θ) is the likelihood function for the specific analysis, in this case given by Eq. 5.6. The parameter θ represents all the nuisance pa- U rameters of the likelihood, that is µ , τB, τC defined in Eq. 5.3 and αs 130 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS defined in Eq. 5.5. Both the nuisance parameters θ and the parameter of interest, µ, occur in terms of the best fit values (maximising the likelihood for given (pseudo) data) assuming all other parameters to be left floating, as θˆ andµ ˆ, respectively. This is referred to as profiling [159]. The con- ditional Maximum Likelihood Estimators (MLE) of θ for a given µ are ˆ denoted as θˆ(µ). For data whereµ ˆ < 0, µ = 0 is used in the denominator as it is the best fit value of µ that is physical. The test statisticq ˜µ is then defined as:    0 ifµ ˆ > µ, 0 ifµ ˆ > µ,  ˆ   2 ln L(µ,θ(µ)) if 0 µˆ µ, q˜µ = = − L(ˆµ,θˆ) ≤ ≤ ˆ  2 ln λ˜(µ) ifµ ˆ µ  L(µ,θˆ(µ))  2 ln ˆ ifµ ˆ < 0 − ≤ − L(0,θˆ(0)) (5.10) where also the upwards fluctuation caseµ ˆ > µ has been separated, since when setting an upper limit, one would not regard data withµ ˆ > µ as representing less compatibility with µ than data withµ ˆ = µ. Note that the test statistic is always evaluated with respect to a given (pseudo) data. Note also thatq ˜µ is a function of µ and the distribution ofq ˜µ for both background only, background + signal pseudo data and observed data will depend on µ.

Full Frequentist Procedure

The full frequentist CLs procedure is based on pseudo experiments. In the pseudo experiment generation, the background and signal event yields in both the signal region and the control regions are randomized, whereas the nuisance parameters are fixed to their MLE with respect to observed data and the µ that is hypothesized. When evaluating the test statistic, the nuisance parameters are however let floating. The auxiliary measurement a appearing in the constraint term Eq. 5.6 is also randomized, defining a so called unconditional ensemble of pseudo experiments.

Correction of Correlation Between Discrimination Variables As is described in Sec. 5.7, a systematic uncertainty, κ, is introduced to account for the possible correlation between the discrimination variables. As κ is highly correlated with τC when modelled in the likelihood as an extra nuisance parameter, another procedure was chosen so as to ensure 5.8. Statistical Procedure for Limit Setting 131 the robustness of the ﬁts. The limit-setting procedure was repeated for κ = 0.6, 1.0 and 1.4, respectively, for each sample. The most conservative limit is then chosen. For the same model, the limits with diﬀerent values of κ typically varied a few percent, with a few varying up to 18%.

Investigations of Statistical Integrity

The CLs method is computationally intensive and the limit setting procedure was performed by the standardized RooStats [160] framework. In order to check the robustness of the results, involving construction of the likelihood, generation of pseudo experiments and a large number of eval- uations of the test statistic involving multidimensional ﬁts, a number of checks were made.

Investigations of Test Statistic Distributions and p-value Distributions

The test statistic pseudo experiment distributions provide an insight into the likelihood construction and the fits. The general features of the distributions, see Fig. 5.14, can be understood as follows. The background only distribution (blue) is located to the right of the signal + background distribution (red), since data that is more compatible with the background only hypothesis than the signal + background hypothesis and thus the background only events have larger values ofq ˜µ. As the signal µ increases, the two distributions are moreover seen to be more and more separated as the difference between the two hypotheses grows. The observed data (black line) is located within the background only distribution as expected since no signal events are observed. The pµ value (red-shaded integral) can be seen to become smaller and smaller for the increasing values of µ, as the hypothesised µ is less and less consistent with data, whilst the p0 (blue-shaded integral) remains fairly constant, as is gives a measure of how consistent data is with the background hypothesis which does not depend on the signal strength to first order. There is a peak at zero for the signal + background distribution, associated with to the upwards fluctuation of pseudo data,µ ˜ > µ. The multiple maxima of the distributions, are due to the discreteness of the event yields as a consequence of the low statistical precision in the signal region A (0 observed events) and control region C (3 observed events). Every region is effectively modelled as a Poisson distribution, and a Poisson distribution with average 3 has already a probability as low as 3% for a yield of 7 events. The most frequent combinations of ≥ 132 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

ModelConfig_with_poi_0 ModelConfig_with_poi_0 ModelConfig_with_poi_0 ModelConfig_with_poi_0 10 10 ModelConfig 10 ModelConfig ModelConfig ModelConfig test statistic data test statistic data test statistic data test statistic data 10

1 1 1

− −1 −1 1 10 10 10

−1 10 − −2 −2 2 10 10 10 −1 −0.5 0 0.5 1 −2 −1.5 −1 −0.5 0 0.5 1 −2 −1 0 1 2 −2 −1 0 1 2 3 4 Profile Likelihood Ratio Profile Likelihood Ratio Profile Likelihood Ratio Profile Likelihood Ratio

ModelConfig_with_poi_0 ModelConfig_with_poi_0 ModelConfig_with_poi_0 ModelConfig_with_poi_0 ModelConfig ModelConfig ModelConfig ModelConfig test statistic data test statistic data test statistic data test statistic data

1 1 1 1

− − −1 −1 1 1 10 10 10 10

− −2 −2 2 −2 10 10 10 10

−2 −1 0 1 2 3 4 5 −2 0 2 4 6 −2 0 2 4 6 8 −4 −2 0 2 4 6 8 Profile Likelihood Ratio Profile Likelihood Ratio Profile Likelihood Ratio Profile Likelihood Ratio

−1 −1 − 10 1 10 −1 10 10

−2 − −2 10 2 10 −2 10 10

−2 0 2 4 6 8 10 −4 −2 0 2 4 6 8 10 12 −4 −2 0 2 4 6 8 10 12 −2 0 2 4 6 8 10 12 14 Profile Likelihood Ratio Profile Likelihood Ratio Profile Likelihood Ratio Profile Likelihood Ratio

ModelConfig_with_poi_0 ModelConfig_with_poi_0 10 ModelConfig_with_poi_0 ModelConfig_with_poi_0 ModelConfig ModelConfig ModelConfig ModelConfig test statistic data test statistic data test statistic data test statistic data

1 1 1 1

−1 −1 − 10 1 −1 10 10 10

−2 −2 − 10 2 −2 10 10 10

0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 18 0 5 10 15 20 Profile Likelihood Ratio Profile Likelihood Ratio Profile Likelihood Ratio Profile Likelihood Ratio

ModelConfig_with_poi_0 ModelConfig_with_poi_0 ModelConfig_with_poi_0 ModelConfig_with_poi_0 10 ModelConfig ModelConfig ModelConfig ModelConfig test statistic data test statistic data test statistic data test statistic data 1 1 1 1

−1 10 − −1 −1 1 10 10 10

−2 10 − −2 −2 2 10 10 10 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 25 Profile Likelihood Ratio Profile Likelihood Ratio Profile Likelihood Ratio Profile Likelihood Ratio

Figure 5.14: Examples of test statistic distributions of background only (blue) and background + signal (red) as described in the text for 10 000 pseudo experiments where the signal model is a monopole of mass 1000 GeV and charge 0.5 gD. The black line represents the data value of the test statistic. The value of µ starts at 0 at the top left ﬁgure (this special case can be neglected as it is not part of the limit setting procedure) and increases (from left-to-right and then row-wise) to µ = 20 at the bottom right plot.

event yields in these regions are thus fairly few and are visible as peaks in the distributions. To test this hypothesis, the limit-setting was repeated with statistical precision in the order of 100 events in region A and C, whereby the distributions became smooth. The existence of nuisance parameters such as systematic uncertainties with a large allowed range adds more degrees of freedom to the test statistic. This is seen when comparing test statistic distributions with low systematic uncertainties to those with larger systematic uncertainties, where the samples with higher systematic uncertainties show more smooth distributions.

A p-value scan is a graph which shows the p0 value and pµ as a function of the hypothesized µ. In 10 % of the models, a slight discontinuity in the expected p-value scan is visible. In a couple of those, the discontinuity was close to the region where the limit was set. In order to make sure 5.8. Statistical Procedure for Limit Setting 133 that this feature did not affect the result, all p-value scans showing this feature was investigated and it was verified that the p0 and the pµ values 0 pµ both varied, in a way such as to preserve the ratio pµ = . In Fig. 5.15, p0 two p-vaue scans are shown, one with a fluctuation in the p0-value and one without. In the figures, the p0 and pµ are denoted CLb and CLs+b, 0 respectively. The pµ is denoted as CLs. It is visible how in the left figure, the pµ-value is varying by the same relative amount as the p0, and the deviation is thus not reflected in the result, the CLs limit.

Frequentist CL Scan for workspace result_mu Frequentist CL Scan for workspace result_mu

Observed CLs Observed CLs 1 1 Observed CLs+b Observed CLs+b p value p value Observed CLb Observed CLb Expected CLs • Median Expected CLs • Median 0.8 0.8 Expected CLs ± 1 σ Expected CLs ± 1 σ Expected CLs ± 2 σ Expected CLs ± 2 σ

0.6 0.6

0.4 0.4

0.2 0.2

0 0 0 1 2 3 4 5 0 1 2 3 4 5 mu mu

Figure 5.15: So called p-value scans for single monopoles of charge 1.5 gD and mass 1500 GeV (left) and 2000 GeV (right), respectively. The y-axis shows the p-value, as deﬁned in Eqs. 5.7 and 5.8, for background only (CLb), signal + background (CLs+b) and the ratio (CLs = CLs+b/CLb). The x-axis shows the hypothesised value of the parameter if interest, µ. The red line at 0.05 denotes where the limit is set, that is at CLs = 5%. The green and yellow bands show the 1 (green) and 2 (yellow) standard deviations of the expected values of CLs in case of that the observed events would equal the expected background, and the median is shown as a dashed line.

Impact of Systematics and Signal Contamination on Limits The effect of the systematic uncertainties on the limit is quantified in Fig. 5.16, where the limit is given as a function of the value of the positive and negative systematic uncertainties, respectively. The general feature of the figure is that for systematic uncertainties larger than 10 15%, − the limits vary on the order of 10 20%. A larger systematic uncertainty − increases the phase space allowing for larger variations in the fit values of both µ and the nuisance parameters, thus allowing for a larger variation of 134 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS the limit. A significant increase in the limit is also visible for the mass and charge point of large negative systematic uncertainty. A large negative systematic uncertainty allows for a low signal efficiency. A larger signal strength is then required to give the event yield needed for a separation of the background only and background + signal hypothesis corresponding to CLs = 5%. For some models, the signal contamination into the control regions C or B is considerate, see Tab. 5.2. A leakage of the signal into a control region could theoretically decrease the limit setting power for any given observed data (in the absence of discovery), since the signal then hypothetically could be fitted also to data in the control regions. The signal contamination into region C ranges from 35% to 48% for the single particle HECOs of charge 20 e. For single monopoles, the signal leakage into region B is large for models of mass 200 GeV and charges 1.0 gD. ≥ No significant difference in the limits between HECOs of charge 20 - 60 e exists, nor between the mass 200 GeV and charges 1.0 gD monopoles ≥ and the other monopole samples, see Fig. 5.17.

Robustness of the Fits and Correlations Between Nuisance Parameters

Due to the relative complexity of the likelihood, with several nuisance parameters and, for some models, a large systematic uncertainty, the correlation between the parameters were investigated to make sure they were U understood. The nuisance parameters µ and τB are highly correlated (the correlation coeffcienct > 0.9). Since the background estimate, µU is given by the yields in the control regions, it is more or less inherent to the ABCD method that µU is correlated with the τ parameters. The large difference in statistical precision between the control regions B and D on one hand and the control region C on the other hand, makes the background estimate much more dependent on the yields in the regions U B and D, which is reflected in the correlation between µ and τB (used in the modelling of the D region as well). To verify this hypothesis, the fits were repeated with input values where the statistical precision in the B, C and D regions were more similar, and the correlation between µU U and τB accordingly decreased and the correlation between µ and τC increased. In addition, all the fits performed in the limit setting procedure were checked to converge. 5.8. Statistical Procedure for Limit Setting 135

Figure 5.16: Limits on the number of signal events vs positive (y-axis) and negative (x-axis, where the values are shown as negative) systematic uncertainty on the signal eﬃciency. The data points are shown in black on top of a coloured surface connecting the points. The data in the plot are for correction factor κ = 1 and for all the mass and charge points for which limits were set, including DY-produced HIPs and DY-produced spin-0 monopoles.

Results Upper limits (at 95% CL) were set on the production cross section of magnetic monopoles and HECOs in regions of high and uniform acceptance as defined in Tabs. 5.8- 5.11. The limits are shown in Fig. 5.17 and are 0.5 fb for all HIP mass and charges. The limits were set on HECOs ∼ in the mass range 200 - 2500 GeV and charge range of 20 - 40 e. On monopoles, the limits were set in the same mass range as HECOs and in a charge range of 0.5 - 2.0 gD with the exception of monopoles of charge 0.5 gD, where limits could only be set on monopoles with masses 1000 ≤ GeV. Limits were also set on Drell-Yan produced HIPs, in the mass range 200 - 2500 GeV and the charge range 10 - 60 e and 0.5 - 1.5 gD, with the exception of HECOs of mass 2500 GeV and charge 60 e as well as monopoles of mass 200 GeV and charge 1.5 gD. These limits are shown 136 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS in Fig. 5.18. The limits are driven by the acceptance, which varies between different mass and charge points, as is described in section Sec. 5.5. Limits were also set on Drell-Yan produced HIPs with a spin-0 interpretation, as presented in Ref. [2]. Monopoles with charges higher than 1 gD and HECOs with charges higher than 17 e were for the first time probed at the LHC. The mass range for monopoles was increased to > 1500 GeV for the first time for any collider search. The search was conducted using the highest collision energies ever at use at a collider. In Fig. 5.19, the limits of this search are compared to earlier collider searches for monopoles, as given in Tab. 1.3.

1 1 Data 2012 Data 2012 0.9 −1 0.9 −1 ∫ Ldt = 7.0 fb ∫ Ldt = 7.0 fb √s = 8 TeV √s = 8 TeV 0.8 0.8 SP Monopole, 0.5 gD SP HECO, 20 e SP Monopole, 1.0 gD SP HECO, 40 e SP Monopole, 1.5 gD 0.7 SP HECO, 60 e 0.7 SP Monopole, 2.0 gD

0.6 0.6

Limit on cross section [fb] 0.5 Limit on cross section [fb] 0.5

0.4 0.4

0.3 0.3 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 m [GeV] m [GeV]

Figure 5.17: Upper limits (at 95% CL) using the CLs method for single HECOs (left) and monopoles (right). The DY limits are set with respect to diﬀerent models parametrized by mass (200, 500, 1500, 2000 and 2500 GeV) and charge as given in the ﬁgure. The lines shown are interpolations between models. 5.8. Statistical Procedure for Limit Setting 137

charge = 20 e mass Aη Bη Cη 0.3< η <0.45 - - 200 | kin| 150 < ET < 200 - - 0.1< η <0.4 - - 500 |kin| 175 < ET < 325 - - 0.15< η <0.55 - - 1000 |kin| 225 < ET < 425 - - 0.15< η <0.6 - - 1500 |kin| 375 < ET < 450 - - 0.25< η <0.45 - - 2000 |kin| 375 < ET < 550 - - 0.15< η <0.5 - - 2500 |kin| 450 < ET < 600 - -

Table 5.8: Fiducial regions for HECOs of charge 20 e and various masses, kin kin given in GeV. The values of ET and EL are also given GeV.The symbol ”-” denotes a region in η where no ﬁducial region of high eﬃciency was found. 138 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

charge = 40 e mass Aη Bη Cη 0.0< η <0.7 1.0< η <1.35 1.55< η <1.95 200 |kin| | kin| |kin| 300 < ET < 775 200 < ET < 650 475 < EL < 750 0.0< η <0.75 1.0< η <1.35 1.55< η <2.0 500 | kin| | kin| |kin| 275 < ET < 850 225 < ET < 700 500 < EL < 875 0.0< η <0.7 1.05< η <1.35 1.55< η <2.0 1000 |kin| |kin| kin| | 325 < ET < 1050 375 < ET < 825 600 < EL < 1025 0.0< η <0.7 1.1< η <1.35 1.55< η <2.0 1500 |kin| | kin| kin| | 400 < ET < 1175 350 < ET < 900 650 < EL < 1150 0.0< η <0.7 1.1< η <1.35 1.55< η <2.0 2000 |kin| |kin| kin| | 450 < ET < 1300 475 < ET < 1000 750 < EL < 1225 0.0< η <0.7 1.15< η <1.35 1.55< η <1.95 2500 |kin| |kin| |kin| 500 < ET < 1425 525 < ET < 1050 800 < EL < 1325

charge = 60 e mass Aη Bη Cη 0.0< η <1.0 1.0< η <1.35 1.55< η <2.0 200 |kin| |kin| kin| | 500 < ET < 1625 350 < ET < 1450 725 < EL < 1650 0.0< η <1.0 1.0< η <1.35 1.55< η <2.0 500 |kin| |kin| kin| | 450 < ET < 1675 400 < ET < 1525 775 < EL < 1725 0.0< η <1.0 1.0< η <1.35 1.55< η <2.0 1000 |kin| |kin| kin| | 550 < ET < 1850 475 < ET < 1525 950 < EL < 1875 0.0< η <1.0 1.0< η <1.35 1.55< η <2.0 1500 |kin| |kin| |kin| 650 < ET < 1950 525 < ET < 1525 1075 < EL < 2050 0.0< η <0.85 1.0< η <1.35 1.55< η <2.0 2000 |kin| |kin| |kin| 725 < ET < 2225 600 < ET < 1525 1150 < EL < 2200 0.0< η <0.8 1.0< η <1.35 1.55< η <2.0 2500 |kin| |kin| |kin| 800 < ET < 2325 675 < ET < 1525 1375 < EL < 2350

Table 5.9: Fiducial regions for HECOs of charge 40 e and 60 e and various kin kin masses, given in GeV. The values of ET and EL are also given GeV. 5.8. Statistical Procedure for Limit Setting 139

Monopoles of charge 0.5 gD mass Aη Bη Cη 0.0 < η < 0.8 1.0 < η < 1.3 1.6 < η < 1.7 200 |kin| | kin| |kin| 125 < ET < 400 150 < ET <400 325 < EL < 425 0.0 < η < 0.65 1.05 < η < 1.25 - 500 | kin| |kin| 125 < ET < 325 225 < ET < 325 - 0.15 < η < 0.55 - - 1000 |kin| 200 < ET < 275 - -

Monopoles of charge 1.0 gD mass Aη Bη Cη 0.0< η <1.0 1.0< η <1.35 1.6< η <1.95 200 |kin| |kin| |kin| 350 < ET < 1525 350 < ET < 1300 900 < EL < 1825 0.0< η <1.0 1.0< η <1.35 1.6< η <1.95 500 |kin| |kin| |kin| 275 < ET < 1750 275 < ET < 1500 825 < EL < 1700 0< η <1.0 1.0< η <1.35 1.55< η <1.95 1000 | kin| |kin| |kin| 275 < ET < 1525 275 < ET < 1500 850 < EL < 1450 0.0< η <1.0 1.0< η <1.35 1.6< η <1.95 1500 |kin| |kin| |kin| 450 < ET < 1375 325 < ET < 1325 725 < EL < 1350 0.0< η <0.7 1.0< η <1.35 1.55< η <1.95 2000 |kin| |kin| |kin| 275 < ET < 1325 400 < ET < 1275 750 < EL < 1225 0.0< η <0.7 1.05< η <1.35 1.6< η <1.95 2500 |kin| |kin| |kin| 350 < ET < 1250 450 < ET < 1225 800 < EL < 1225

Table 5.10: Fiducial regions for monopoles of charge 0.5 gD and 1.0 gD kin kin and various masses, given in GeV. The values of ET and EL are also given GeV. The symbol ”-” denotes a region in η where no ﬁducial region of high eﬃciency was found. 140 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

Monopoles of charge 1.5 gD mass Aη Bη Cη 0.15< η <1.0 1.0< η <1.35 1.75< η <1.9 200 kin| | |kin| |kin| 825 < ET < 1800 775 < ET < 1500 1700 < EL < 2625 0.0< η <0.9 1.0< η <1.35 1.55< η <1.95 500 |kin| |kin| |kin| 600 < ET < 2175 650 < ET < 1500 1675 < EL < 2775 0.0< η <0.95 1.0< η <1.35 1.55< η <1.95 1000 |kin| |kin| |kin| 525 < ET < 2100 575 < ET < 1525 1450 < EL < 2775 0.0< η <1.0 1.0< η <1.35 1.55< η <1.95 1500 |kin| |kin| |kin| 500 < ET < 2025 525 < ET < 1525 1525 < EL < 2775 0.0< η <1.0 1.0< η <1.35 1.55< η <1.95 2000 |kin| |kin| |kin| 500 < ET < 2025 500 < ET < 1525 1325 < EL < 2775 0< η <0.8 1.0< η <1.35 1.55< η <1.95 2500 | kin| |kin| |kin| 425 < ET < 2300 500 < ET < 1500 1325 < EL < 2775

Monopoles of charge 2.0 gD mass Aη Bη Cη 0.25< η <0.6 1.0< η <1.2 - 200 |kin| |kin| 1200 < ET < 1625 1425 < ET < 1725 - 0.1< η <0.7 1.0< η <1.3 1.75< η <1.85 500 |kin| |kin| |kin| 1150 < ET < 2450 1250 < ET < 1600 2575 < EL < 2850 0.05< η <0.8 1.0< η <1.3 1.75< η <1.85 1000 |kin| |kin| |kin| 1075 < ET < 2325 1150 < ET < 1600 2525 < EL < 2850 0.0< η <0.75 1.0< η <1.3 1.8< η <1.95 1500 |kin| |kin| | kin| 950 < ET < 2375 1050 < ET < 1600 2325 < EL < 2850 0.0< η <0.75 1.0< η <1.3 1.75< η <1.95 2000 |kin| |kin| |kin| 875 < ET < 2375 1000 < ET < 1600 2275 < EL < 2850 0.05< η <0.75 1.0< η <1.35 1.75< η <1.95 2500 |kin| |kin| |kin| 850 < ET < 2400 975 < ET < 1525 2150 < EL < 2850

Table 5.11: Fiducial regions for monopoles of charge 1.5 gD and 2.0 gD kin kin and various masses, given in GeV. The values of ET and EL are also given GeV. The symbol ”-” denotes a region in η where no ﬁducial region of high eﬃciency was found. 5.8. Statistical Procedure for Limit Setting 141

3 10 Data 2012 Data 2012 −1 −1 ∫ Ldt = 7.0 fb ∫ Ldt = 7.0 fb DY Monopole, 0.5 gD 2 2 10 √s = 8 TeV 10 √s = 8 TeV DY Monopole, 1.0 gD DY Monopole, 1.5 gD

10 Limit on cross section [fb] Limit on cross section [fb] 1 DY HECO, 10 e DY HECO, 20 e DY HECO, 40 e DY HECO, 60 e •1 10 1 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 m [GeV] m [GeV]

Figure 5.18: Upper limits (at 95% CL) using the CLs method for Drell- Yan produced HECOs (left) and monopoles (right). The limits are set with respect to diﬀerent models parametrized by mass (200, 500, 1500, 2000 and 2500 GeV) and charge as given in the ﬁgure. The lines shown are interpolations between models. 142 Chapter 5. Search for Magnetic Monopoles and HECOs at ATLAS

3 10

2 pp 10 pp pN 10 ep + • e e 1

•1 10

•2 10

•3 10 Limits on production cross sections [pb] •4 ATLAS 2012 10

•5 10

2 3 4 10 10 10 10 s [GeV]

Figure 5.19: Overview over upper limits on production cross section for HIPs at colliders of different centre of mass energies (√s). The searches for which the limits are given are listed in Tab. 1.3, together with the mass and charge ranges for which the limits are valid. For searches with several different limits quoted for different charges, the most stringent limit is shown in the figure. The limit corresponding to the search presented in this thesis is marked with “ATLAS 2012”. Chapter 6

Search for Magnetic Monopoles in Polar Volcanic Rocks

This chapter concerns the search for magnetic monopoles described in Paper III. A short review of the analysis will be given and a more detailed discussion of the calibration of the SQUID magnetometer, which I was responsible for, follows. I was also responsible for the major part of the data taking and also made general editorial contributions to the attached paper [3]. At the end of the chapter the results will be presented.

6.1 Introduction

Magnetic monopoles are predicted by many GUT theories as described in Sec. 1.3. Introducing magnetic monopoles would through the Dirac argument explain the electric charge quantisation problem, as discussed in Sec. 1.3. In addition, Maxwell’s equations would become symmetric, as described in the same section. The open question is therefore why they have not been seen. A possible explanation could be that they are too heavy to be produced at a collider. Colliders are sensitive to monopoles with masses up to the TeV scale [55, 75]. Alternatively, their density could be low so as to escape certain searches in matter. This work explores the hypothesis that monopoles were present at the formation of the Earth, for example in stardust, and would have become trapped in the early molten Earth. Such monopoles would, through

143 144 Chapter 6. Search for Magnetic Monopoles in Polar Volcanic Rocks

Figure 6.1: A schematic overview of the experimental setup with the SQUID detector. Samples are measured at different positions in the z direction, in this picture along the conveyor belt. It should be noted that the SQUID used in this study did not operate with a conveyor belt but instead a setup with a sample holder fixed to a rod moving along the z-axis was employed. The figure is from from Ref. [78].

geomagnetic processes, be most likely observed in polar regions, as is explained below. There are non-relativistic quantum calculations suggesting that monopoles could bind to atomic nuclei [161]. Given the chemical differentiation of the Earth, the possible existence of monopoles trapped inside the Earth would then be most likely close to the core of the Earth. Paleomagnetic data indicate that the Earth has had a magnetic dipole ﬁeld since at least 3.5 billion years [162, 163, 164]. This would imply ∼ that magnetic forces on the monopoles were competing with the gravitational forces, and that monopoles would be more likely to be found along the magnetic ﬁeld axis of the Earth. The equilibrium position, which depends on the mass and the charge, can range all the way up to the mantle. Volcanic rocks from “hotspots”, places where the mantle is believed to contain material from deep regions, have therefore been examined. The volcanic regions are also required to be of high latitude. Under the given assumptions these samples are likely to contain magnetic monopoles. 6.1. Introduction 145

Experimental Procedure

The aim of the experiment was to measure the magnetisation of the volcanic rocks by means of a magnetometer which is able to discern a monopole magnetic field from a dipole magnetic field. Samples of crushed volcanic rocks, placed into plastic containers to fit the experimental device, were used. A brief outline of how a SQUID magnetometer can be used in monopole searches can be found in Sec. 2.4 and a schematic overview is presented in Fig. 6.1. A rock sample is moved along the z axis of the detector, through the pick-up coils (the superconducting loops). The current in the pick-up coils are measured at three different z positions of the sample: before, inside and on the other side of the pick-up coils.

Calibration of the SQUID Detector

A calibration of the SQUID was carried out during the same data taking period as the one where volcanic rocks were measured. It was performed by measuring the response of the detector for a set of solenoids with known currents so as to produce dipole fields with known magnitudes. A long solenoid is equivalent to a magnetic dipole with plus and minus charges at each end. Naively the magnetic moment p = g d where g is · the pseudocharge and d is the dipole length. For a solenoid, p = NIS, where I is the current, S is the surface area and N is the number of turns. For a given solenoid p is thus well known allowing g to be determined. The solenoid used in this study and their corresponding currents and pseudocharges are given in Tab. 6.1. The result of the calibration is shown in Fig. 6.2, where output current amplitudes are shown as a function of the z position of the calibration sample. As can be seen, the magnetometer is not sensitive to the gD = 0.115 pseudocharge field. This does not constitute a problem since the search does not intend to probe regions of such low charge. Since it is the plateau value that is proportional to the magnetic field, a finer granularity in z was used than for the volcanic rock samples, where the main purpose of the measurements was to find a possible persistent current of significant amplitude. Had such a current been found, a more detailed measurement had been carried out on that sample. The background was estimated through measurements on empty plastic containers, and subtracted from the calibration measurements. Fig. 6.3, shows a linear fit to the plateau values. The uncertainties for sample 2 and 3 are not visible in 146 Chapter 6. Search for Magnetic Monopoles in Polar Volcanic Rocks

Calibration sample 1 2 3 4 Solenoid current [µA] 0.01 0.1 1.0 10 Pseudocharge [gD] 0.115 1.15 11.5 115

Table 6.1: The solenoid calibration samples used in this study, with currents and corresponding magnetic dipole pseudocharges, g, as described in the text.

Calibration sample 2 3 4 Plateau value [arb] 4 10−7 4 10−6 3.6 10−5 · · · Uncertainty 1 10−7 0.2 10−6 0.1 10−5 · · · Table 6.2: Plateau values and uncertainties for the three calibration samples used in the calibration. the graph because of their small values relative to the scale of the figure, but the plateau values and the corresponding uncertainties are instead given in Tab. 6.2. The uncertainties were estimated as the largest difference between a pair of measurements in the plateau region. In the linear fit, only samples 2, 3 and 4 were used. The χ2/k, where k is the number of degrees of freedom, of the fit was 0.07. The calibration shows that the magnetometer response is linear in the sensitive region of the search.

Data Taking and Analysis The magnetisation of rock samples from 14 different “hotspots”, in total 23.4 kg, was measured. Fig. 6.4 shows the persistent current expressed in units of corresponding monopole charge gD. The top graph shows the currents for all samples in the search. In the range from 0.1 to 0.1 gD, the − distribution is Gaussian and has a mean value of 0.002 0.002 gD. There − ± are small non-Gaussian tails outside this range. The bottom figure shows the current for five samples for repeated measurements. These were the only samples out of the total 678 for which the measured monopole charge deviate more than 0.25 gD from zero. The largest values correspond to ± candidate 1 and 2, and are 0.8 gD and 1.6 gD, respectively. However, these samples have a total magnetisation equivalent to a magnetic charge > 5 10 gD, which is close to the limit beyond which measurements are known 5 to be unreliable, 1.5 10 gD. Repeating the measurements for different · orientations relative to the SQUID apparatus yielded results consistent with the zero magnetic monopole charge hypothesis. Given the above, it 6.1. Introduction 147

Ie-7 Ie-7

(a) (b)

Ie-6 Ie-5

Figure 6.2: Magnetometer response (current amplitude in arbitrary units) to calibration samples with known magnetic dipole strength as presented in Tab. 6.1, as function of z position. The diﬀerent ﬁgures correspond to calibration sample 1 (a), 2 (b), 3 (c) and 4 (d), respectively. 148 Chapter 6. Search for Magnetic Monopoles in Polar Volcanic Rocks

Figure 6.3: Linear ﬁt to calibration sample plateau values as described in the text. is clear that no reproducible evidence for monopoles were found in these samples.

Results Limits on the monopole density in polar igneous rocks of 9.8 10−5/gram · were set at 90% conﬁdence level. In a simple model this gives a limit of 1.6 10−5/gram in the matter averaged over the whole Earth. A compa- · rable limit was quoted for a search with meteorites which also has some sensitivity to the existence of monopoles at the Earth’s formation [82]. In this search, 112 kg of meteorite samples were examined to give a concentration limit of < 2.1 10−5/gram at 90% conﬁdence level. × 6.1. Introduction 149

) 2 1.5D 1 0.5 0 •0.5 •1 •1.5 •2 1 2 3 4 5 persistent current (g candidate number

Figure 6.4: Measurements of persistent current for all samples volcanic rocks included in the search. The top figure shows the persistent current shown in terms of the corresponding monopole charge for all samples in the search. The bottom figure shows the persistent current for repeated measurements of the persistent current for five samples with high values. The current is expressed in units of corresponding monopole charge gD. The figure is from the attached paper [3]. 150 Chapter 7

Summary and Outlook

Magnetic monopoles arise naturally in many GUT theories and address several open questions in particle physics of today, such as the quantisation of electric charge. HECOs are conceivable within many BSM theories, for example as Q-balls. As the EM coupling constants for HIPs are too large as to allow perturbative expansion, estimations of monopole production cross sections are difficult to carry out. In addition, this also makes any estimations of their abundance in the Early Universe unreliable, along with the annihilation rate and thus the abundance in the Universe of today. This motivates searching for HIPs using both colliders, cosmic rays and matter. The research presented in this thesis includes a search for HIPs in ATLAS, LHC, and a search for monopoles in volcanic polar rocks. The search for monopoles and HECOs at ATLAS was conducted using a customized trigger and selection variables optimized for the non- standard particle signature in ATLAS. The dataset corresponds to an integrated luminosity of 7.0 fb−1 and a centre-of-mass energy os 8 TeV. No events were observed and 95% CL upper limits on production cross- sections were set for monopoles and HECOs of masses 200-2500 GeV and charges in the range 0.5 - 2.0 gD and 10 - 60 e, respectively. Magnetic monopoles were also sought in polar volcanic rocks using a SQUID magnetometer at ETH, Zürich. No candidates were found, leading to limits on the monopole density in polar igneous rocks of 9.8 × 10−5/gram. Future searches for HIPs at the LHC experiments with higher centre- of-mass energies could probe masses up to 6000 GeV [148]. The different experiments, ATLAS, CMS, LHCb, MoEDAL and ALICE have different sensitivities in terms of charge, due to different designs of the detectors.

151 152 Chapter 7. Summary and Outlook

Early estimates of the sensitivities (assuming 14 TeV centre-of-mass energy) are summarised in Fig. 7.1. The MoEDAL [94] detector is a dedicated monopole and exotic particle detector located directly near the LHCb intersection point of the LHC and can thus record HIPs which would otherwise have stopped in supporting structure or even the beam pipe of the larger detectors. A new addition to the MoEDAL, the Very High Charge Catcher, will increase its sensitivity for high charges. ALICE has a low budget supporting structure and does accordingly also show a good sensitivity for high charge. By extracting the beam pipe, monopoles of very high charge that could have stopped here can be detected, and beam pipe experiments are thus sensitive to much higher charges than the detectors [165]. In the search for HIPs at ATLAS presented in this thesis, the major constraint in terms of sensitivity was the L1 trigger, where no track information is available and thus a electron/photon trigger had to be used. Including track information at the L1 is planned for the so called Phase-2 of LHC, scheduled for around year 2024 - 2026. This would allow for a customized HIP trigger at all levels, which could increase the sensitivity for high mass and high charge HIPs signiﬁcantly. Another possibility to investigate would be to use the LAr timing to estimate the TOF, which for HIPs can be used as a discriminator, as is described in Sec. 1.4. At the time of the data-taking of the research presented in this thesis, no information could be read out from saturated Pixel detector channels, which otherwise possibly could have been used as a discriminator for HIPs. In the current system, this information is available both in collision data and in the simulation. It is diﬃcult to quantify the increase in sensitivity with these approaches since a full simulation including the new techniques would be needed. Matter searches for monopoles will continue to constitute an important complement to collider and cosmic ray searches for monopoles. Natu- rally, every time a new material is found which can be assumed to contain monopoles, it must be examined. 153

14 TeV PYTHIA Drell•Yan, m=1000 GeV, 10 events in acceptance 14 TeV PYTHIA Drell•Yan, m=1000 GeV, 10 events in acceptance 106 106

105 105 ALICE ALICE 104 104

3 3 cross section (fb) cross section (fb) 10 10 MoEDAL 102 MoEDAL 102 LHCb LHCb 10 ATLAS and CMS beam pipes 10 ATLAS ATLAS 1 CMS 1 CMS •1 •1 10 0 2 4 6 8 10 12 14 10 0 100 200 300 400 500 600 Magnetic charge (g ) D Electric charge (e)

Figure 7.1: HIP pair production cross section sensitivities for obtain- ing 10 events with at least one HIP inside the detector acceptance, as a function of HIP magnetic (left) and electric (right) charge, assuming m = 1000 GeV and a Drell-Yan pair production mechanism with 14 TeV pp collisions. Integrated (instantaneous) luminosities are taken as 20 fb−1 (5 1033 cm−2s−1) for ATLAS and CMS, 2 fb−1 (5 1032 cm−2s−1) for × × LHCb and MoEDAL and 0.004 fb−1 (5 103 cm−2s−1) for ALICE. The × ﬁgures are from Ref. [148]. 154 Svensk sammanfattning

Elementarpartikelfysik ärvetenskapen om universums minsta best˚ands- delar och hur de växelverkar med varandra. Standardmodellen ärnamnet p˚aden modell som framg˚angsrikt beskriver detta. Vid upprepade tillfällen har standardmodellens förutsägelserblivit bekräftadeav experimentella observationer. Overensstämmelsenhar¨ ofta visat imponerande högpre- cision. Lika viktigt att framh˚allaärdock att standardmodellen inte kan vara en komplett teori, d˚aden t ex misslyckas med att förklarakällantill viktiga observationer som förekomsten av det som kallas mörkmateria, samt inte p˚an˚agotframg˚angsriktsättlyckas att förenakvantmekanik med Einsteins allmännarelativitetsteori som beskriver gravitationen. Stan- dardmodellen inneh˚allerinte heller n˚agonförklaringtill varförelektrisk laddning ärkvantiserad. Som ett resultat av standardmodellens ofullständighethar m˚anga nya teorier framkommit, s˚akallade bortom standardmodellen-teorier. Exper- imentell partikelfysik handlar idag om att, förutomatt med bättre precision mätastandardmodellens observabler, verifiera eller falsifiera före- komsten av de partiklar som de nya teorierna förutsäger. I m˚angafall handlar det om att begränsaparameterrummet, i form av t ex massa och laddning, förde nya teoriernas partiklar. I flera bortom standardmodellen- teorier förekommer magnetiska monopoler samt partiklar med högmassa och högelektrisk laddning (HECO-partiklar). Existensen av monopoler skulle ha m˚angaintressanta implikationer, t ex förklaraskvantiserin- gen av den elektriska laddningen. En annan tilltalande konsekvens är att Maxwells ekvationer, som beskriver klassiska elektromagnetiska fält, skulle bli symmetriska i och med införandetav monopoler. The Large Hadron Collider (LHC) ärvärldensstörstapartikelaccel- erator och generar masscentrumsenergier p˚a13 TeV. Genom att kollid- era protoner med denna energi kan nya partiklar bildas och detekteras. LHCs störstadetektorer heter ATLAS och CMS och ärbyggda föratt

155 156 Svensk sammanfattning kunna mätam˚angaolika sorters elementarpartiklar. I juli 2014 upptäcktes Higgs-partikeln med hjälpav dessa detektorer. I forskningen som redovisas i denna avhandling, handlar tv˚aprojekt om ATLAS-detektorn. Det förstahandlar om triggern, som ärett selek- tionssystem föratt väljaintressanta kollisioner medan detektorn ärig˚ang. Detta ärväldigtviktigt ur synpunkten att de flesta kollisioner som sker inte ärav intresse förvidare fysikanalys, och att spara alla kollisioner skulle ta oerhördamängder av lagringsutrymme i anspr˚ak,samt ställa enorma krav p˚adataöverföringsinfrastruktur. Min forskning handlade om att utveckla de d˚avarande triggrarna som ett led i förberedelserna för den ökade luminositeten som var att vänta 2012. Triggersysyemet ärin- delat i tre niv˚aeroch jag undersöktetriggers p˚aförstaniv˚an,Level-1 (L1). Mitt förstaprojekt handlade om att utveckla en elektron-fotontrigger som tar detektorns geometri med i beräkningen. Högreenergitrösklarkunde införasförvissa geometriska regioner dären partikel som rörsig genom detektorn behövtinteragera med en mindre mängdmaterial och därmed förloratmindre energi, i jämförelse med en annan geometrisk region. P˚a detta sättkunde antalet kollisioner som valdes ut av triggern minskas medan effektiviteten i stort bibehölls. Mitt andra projekt handlade om en ny trigger som väljerut kollisioner med stor rörelsemängdsobalans i planet vinkelrättmot str˚alröret. En s˚adanobalans kan t ex uppkomma d˚apartikar bildas som inte interagerar med detektorn, s˚asomneutriner eller hypotetiska mörkmateriapartiklar. Den nya triggern användersig av en modell förhur rörelsemängdsobalansenser ut förkollisioner där en ickeinteragerande partikel inte förekommer, och kollisionen allts˚ainte ärintressant. Genom att användasig av denna information kunde triggern görasmer effektiv förde intressanta kollisionerna. Mitt sista projekt ang˚aendetriggern handlade om en vidareutveckling av denna nya trigger, därjag även utvärderadeen h˚ardvaruutveckling som skulle behövas för att implementera denna. Det andra projektet vid ATLAS-detektorn handlade om att leta efter magnetiska monopoler och HECO-partiklar (HIP-partiklar). HIP st˚arför Highly Ionising Particles, högjoniserande partiklar, och definieras av sin högaladdning, 0.5 gD eller 10 e, och stora massa, 200 GeV. Dira- ≥ ≥ ≥ claddningen gD ären enhet förmagnetisk laddning. Föratt ˚astadkomma detta krävdesen noggrann utredning av HIP-partikarnas interaktion med detektorn, eftersom HIP-partiklarna inte tillhörde standardsignaturer s˚asomfotoner eller myoner som de flesta analyser använder,och som därmedärvälstuderade. En specialutformad trigger som användersig Svensk sammanfattning 157 av HIP-partiklarnas sp˚ari en av sp˚ardetektorerna,TRT, användesföratt göraen förstaselektion av kollisioner. De tv˚aeffektivaste och därmedvik- tigaste selektionsvariablerna användersig av HIP-partiklarnas speciella signatur i TRT-detektorn samt i den elektromagnetiska kalorimetern. I TRT-detektorn, ger HIP-partiklarna upphov till m˚angahögtröskelträffar, som annars bara orsakas av relativistiska partiklar som elektroner genom överg˚angsstr˚alning. I HIP-partiklarnas fall ärdet deras högajoniser- ing som ger upphov till högtröskelträffarna. Den förstaselektionsvari- abeln ärförh˚allandetmellan hög-och l˚agtröskelträffari TRT-detektorn. I den elektromagnetiska kalorimetern joniserar HIP-partiklarna atomerna i detektormaterialet i sin närmasteomgivning, men ger till skillnad fr˚an elektroner och fotoner, inte upphov till n˚agonelektromagnetisk skur. Denna specifika signatur användsi den andra selektionsvariabeln, som bygger p˚abredden av det s˚akallade kluster som joniseringen ger upphov till i den elektromagetiska kalorimetern. Jag var bl a ansvarig för att generera simulerad kollisionsdata förHECO-partiklar, göratriggeref- fektivitetsgrafer, utveckla en algoritm föratt hitta högacceptansregioner förolika HIP-partikelmodeller samt förden statistiska behandlingen av data som innebar att övregränserp˚ade olika HIP-partiklarnas produk- tionsgränssittsattes. Gränsernap˚atvärsnittenär0.5 fb föralla HIP- partiklar, med avvikelser p˚an˚agraprocent. Gränserp˚atvärsnittetsattes p˚aHECO-partiklar i massintervallet 200 - 2500 GeV och med laddning 20 - 40 e. Förmonopoler sattes gränserp˚apartiklar med samma massor som HECO-partiklar, och med laddningar 0.5 - 2.0 gD, med undantag av monopoler med laddningen 0.5 gD, därtvärsnittsgränser bara kunde sättasförpartiklar med en massa 1000 GeV. ≤ Det tredje forskningsprojektet som presenteras i denna avhandling berörocks˚amagnetiska monopoler. Iställetföratt söka efter dem i par- tikelkollisioner, undersöktesvulkaniska stenar, vars atomer monopoler antas ha kunnat binda till i ett tidigt stadium av jordens historia. Om monopoler fanns i den materia som jorden bildades av, skulle de pga av sin högamassa kunna antas vara belägnanärajordens innersta kärna. P˚agrund av sin magnetiska laddning, skulle dock jordens magnetfält kunna föramonopolen närmarejordens yta om den befann sig nära mag- netfältetsaxel. Stenar fr˚anvulkaner nära polaromr˚adenaundersöktes därföri en magnetometer som kan skilja mellan dipol- och monopolfält. Inga monopoler hittades och en övregränsp˚adensiteten av monopoler i polarvulkaniska stenar, 9.8 10−5/gram, sattes. · 158 References

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1 In 2011, the ATLAS Experiment [1] at the CERN Large Hadron Collider (LHC) collected 5.25 fb− 1 of data for proton-proton collisions at √s = 7 TeV and 158 µb− of data for lead-lead collisions with nucleon-pair center of mass energy √sNN = 2.76 TeV (prior to any data quality cuts). The goal of the miss ATLAS missing transverse momentum (ET ) triggers [2, 3] is to select events with an imbalance in the total measured momentum due to the presence of particles invisible to the detector. These include neutrinos, which are produced in the decay chains of Standard-Model particles such as the W and Z, heavy quarks, and the Higgs boson. Such events can also arise from the presence of non-interacting particles predicted by theories Beyond the Standard Model, such as the lightest SUSY particle. In offline miss analysis the full detector information can be accessed to get an optimum determination of ET . At the trigger level, however, both computing time and access to the detector information is limited. In 2011, the ATLAS trigger used calorimeter cell positions and the energies they measured in an event to obtain a good approximation of the measurable missing total transverse momentum in that event. In this approach, the components of the missing transverse momentum vector, Emiss, are defined as E = Σ E sin θ cos φ T 6 x − i i i i and Ey = Σ E sin θ sin φ where the sum is over all calorimeter cells i (or grouping of cells i, depending 6 − i i i i on the granularity of information available at the trigger level in which the calculation is being done), Ei is the energy measured in cell i, θi is the angle between the cell i position unit vector v~i (which points from the center of the ATLAS detector to cell i) and the beam axis, and φi is the angle between the projection of v~i onto the plane perpendicular to the beam axis and the horizontal axis pointing towards miss 2 2 the center of the LHC ring. E is defined as (E ) + (Ey) and is used to select candidate events for T 6 x 6 further study. q The scalar sum of the calorimeter cell energies times the projection of their position unit vectors onto the plane perpendicular to the beam axis, ΣET = ΣiEisin θi, can be used as an indication of a hard scatter having taken place, and is therefore also potentially a useful quantity with which to detect interesting events. miss ET and ΣET are both determined by summing over the full calorimeter. Even in events where there are no non-interacting particles produced, imperfect calorimeter resolution will give rise to non-zero miss values of ET . Greater energy deposit in the calorimeters results in larger ΣET and larger calorimeter miss fluctuations, yielding more events passing ΣET and ET trigger thresholds. For large bunch densities, multiple proton-proton interactions occur in a single bunch crossing, each depositing energy in the calorimeters. LHC beam luminosity for proton-proton collisions increased during 2011, so that µ , the h i average over a fill of the Poisson mean number µ of beam interactions per bunch crossing, typically varied from about 7 to 15, but started at about 3 in early 2011 and went as high as 30 in one fill (though the latter had beam conditions very different than was typical for 2011). As this “pileup” contribution to the calorimeter energy measurement increases, in the absence of other modifications to mitigate this ef- miss fect, the ET trigger thresholds must be raised or prescales (the inverse of the fraction of passing events retained) increased to keep trigger rates below the maximum that the system can record. A new type of trigger, using missing transverse momentum significance (XS), was therefore introduced in 2011 to miss miss miss accept some events with signal ET below that of the ET trigger threshold. In XS triggers, the ET resolution in an event is parameterized as a function of ΣET in that event, and the trigger criterion is the miss ratio of ET to its resolution. The following sections describe the transverse momentum triggers and assess their performance in the 2011 data-taking period. The largest fraction of LHC proton-proton events are collisions without miss large momentum transfer, followed by two-jet events from hard parton scatters. The ET trigger rate is miss dominated by mismeasurement of these events, even though they do not have real ET . Trigger behavior for event samples selected with minimal requirements is therefore one aspect of trigger performance studied here. Samples rich in W decays to lepton and neutrino events are used to determine the efficiency

1 of the trigger to select events with real invisible particles. Other characterizations of performance include how well the quantities calculated by the triggers match the respective offline quantities, how well the trigger performance matches what is expected from simulations, and how pileup affects the signal efficiency and background rejection. These triggers were stable and robust, even in the highest 2011 pileup conditions, though some threshold and prescale adjustments had to be done for the higher luminosities. The 2011 data showed that, in the absence of other changes, further luminosity increase would require unacceptably high thresholds or rates. The 2011 data were used to identify the critical issues that needed to be addressed to improve performance under the higher luminosity conditions of 2012 and beyond.

2 Data selection and simulation

The ATLAS trigger system [4] consists of three levels, called Level 1 (L1), Level 2 (L2) and Event Filter (EF). Starting with collisions between particle bunches in the LHC which can be separated by as little as 25 ns (but typically 50 ns in 2011), the trigger selects about 300 Hz of events for permanent storage. The 2011 ATLAS data are divided into data-taking periods, labeled A through N, during each of which conditions of the detector were kept fairly constant. Events selected by a random trigger on colliding bunches, used throughout 2011, provide the sample used to study the bulk of the transverse momentum triggers, and are referred to as the “zero-bias” data sample. Two sets of events rich in leptonic W decays are used to study trigger efficiency for events with real Emiss. W eν events are selected with triggers requiring electron candidates with transverse T → momentum of at least 14 GeV at L1 and 20 GeV at L2 and EF, or 16 GeV at L1 and 22 GeV at L2 and EF. Offline cuts require the electron candidate to be isolated, in the well-instrumented calorimeter region ( η < 2.47 excluding 1.37 < η < 1.52), and to have transverse momentum greater than | | | | 25 GeV. The events must have at least one primary vertex with at least 3 tracks and the electron candidate track must come within 10 mm of a primary vertex. The mass of the reconstructed W candidate W W 4-vector in the transverse plane (mT ) is required to be greater than 80 GeV, where mT is defined as 2pl Emiss[1 cosφ(pl , Emiss)], pl is the lepton transverse momentum, and φ(pl , Emiss) is the angle in T T − T T T T T qthe transverse plane between pl and Emiss. The W µν candidate events are selected by triggering on T T → a muon candidate with transverse momentum of at least 11 GeV at L1 and 18 GeV at L2 and EF. A pri- W mary vertex with at least 3 good tracks is required and mT must be from 40 to 95 GeV. The W selection criteria are chosen to minimize the background when comparing data with simulated events, which do not contain background. In particular, the mW cut is set high for W eν candidate events in order to T → suppress QCD background, which is significant in this channel. Events are simulated with the ATLAS simulation framework [5] using the PYTHIA6 [6] program for event generation. Minimum-bias events, which simulate the bulk of the inelastic proton-proton interactions, are used to compare with the zero-bias data sample. The ATLAS MC11 AMBT2B CTEQ6L1 tune [7] with the CTEQ6L parton distribution functions [8] is used for minimum-bias events. W events are simulated using the the ATLAS MC11 AUET2B MRST LO** tune [7]. The GEANT4 [9] software package is used to simulate the passage of particles through the ATLAS detector. Selection criteria identical to those imposed on the data are applied to the simulated W events. How- ever, some differences between measured and simulated distributions are likely to arise from background events surviving the data event-selection cuts. Comparisons are therefore done for the two different W decay modes, as the electron and muon samples will have very different backgrounds.

2 3 The transverse momentum triggers

The L1 ATLAS calorimeter trigger uses firmware on custom electronics to determine ΣE , E and Ey T 6 x 6 from summed coarse-grained calorimeter elements called trigger towers (summing over projective regions of approximate size ∆η ∆φ = 0.2 0.2 for η < 2.5 and larger and less regular in the more × × | | miss forward region [4]) and compare the values with thresholds for the XE (ET ), TE (ΣET), and XS trigger thresholds. The nomenclature is such that L1 XS30 means a Level 1 XS threshold of 3.0 while L1 XE30 miss and L1 TE500 have Level 1 thresholds of 30 GeV for ET and 500 GeV for ΣET, respectively. The L2 and EF level triggers are software based and run on computer farms. Bandwidth limitations and the high granularity of the cell level information make it impossible to access the complete fine-grained cell-level data from the ATLAS calorimeters at the Level 2 trigger. For this reason, in 2011 the L1 information was retrieved and used at L2. Except for some minor differences in implementation (for example, whereas miss L1 uses a look-up table to determine from the x and y momentum sums whether the ET threshold was passed, L2 uses the square root of the sum of the components squared) the L2 results shown below use the L1 values, and L1 and L2 will refer, for the most part, to the same algorithm and values. The 2011 EF algorithm used the full granularity of the 188 000 calorimeter cells. Muon infor- ∼ mation is available at both L2 and EF but was not used in active 2011 triggers. The best ATLAS offline determination of transverse momentum includes muons as well as hadronic calibration to correct for the difference in calorimeter response to energy deposit by electromagnetic and hadronic processes [10, 11, 12, 13]. As the trigger quantities used in 2011 did not include such corrections, their performance is evaluated by comparing them with offline quantities not including these corrections. miss Figure 1 compares the L1 and EF ET and ΣET distributions for events selected in 2011 by a random trigger during beam crossings with a simulated sample of minimum-bias events of similar µ . The peaks h i of the distributions, which account for the bulk of events, agree well with the data, but the spread in the data distributions are significantly higher, especially for ΣET. There are several possible reasons for these differences. A previous ATLAS study [10] has found that PYTHIA6 does not fully describe the observed miss offline ΣET and ET high-energy tails and that these are better matched in PYTHIA8. Another source of miss more high ET and ΣET events than expected from simulation are occasional noisy cells that give large signals. Individual bad cells can be flagged and removed at EF level, but not at L1. Events where a large number of cells give spurious energy can be detected offline, but affect the trigger distributions shown here. Finally, the measured ΣET distributions are sensitive to the precise shape of calorimeter pulses, the details of the pileup structure, and the noise suppression scheme used. When the luminosity increases, there are, on average, more interactions in a bunch crossing, adding more energy to the calorimeters and causing both average calorimeter energy deposit and fluctuations in energy deposit to increase; this is called “in-time” pileup. In order to meet the necessarily strict signal timing requirements while also optimizing cell energy determination, calorimeter pulses are shaped by differentiation and integration, producing a quickly-rising pulse followed by a long opposite-sign tail [14]. The pulses last longer than the time between bunch crossings, so that calorimeter energy in past bunches can add positive or negative signal to energy measured in the current bunch crossing, thereby changing average cell energies and increasing measurement fluctuations; this is called “out-of-time” pileup. A uniform threshold of about 1 GeV was used for all trigger towers at L1 in 2011. The granularity at which L1 energy was measured was also about 1 GeV, as is visible in some of the distributions shown below. At EF level, in order to protect against possible spurious large negative values in individual cells, miss the 2011 EF algorithm did not include in the calculation of ET and ΣET any cells with energy less than 3 times the cell noise distribution width, σcell. Rejection of all cells or towers with negative noise fluctuations while retaining those with large positive fluctuation causes an offset in the ΣET distribution miss but has negligible impact on the ET distribution. This offset strongly depends on the detailed shape

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miss miss Figure 1: L1 ET (top left), L1 ΣET (top right), EF level ET (bottom left) and EF level ΣET (bottom right) distributions for events triggered on random colliding bunches compared with expectations from simulation. of the noise distributions and hence also on the in-time and out-of-time pileup. The parameters used for determining calorimeter signals at L1 can in principle be tuned for the particular µ at which data is recorded, but the non pileup values were used for L1 throughout 2011. At EF level, the trigger has access to cell energies determined in Digital Signal Processors with sophisticated algorithms using pulse-shape information. In order to deal with the increasing µ, in the middle of 2011 the constants used in shape parameterization were changed and the σcell definitions were modified to include a pileup-dependent term. Like the energy deposit due to pileup, the resulting σcell values vary significantly with cell position. For example, for µ = 8, the hadronic calorimeter σcell ranges from tens of MeV in the central part of the calorimeter, to hundreds of MeV at η 2 to several GeV at η 4. These changes in turn caused miss | | ∼ | | ∼ differences in the measured ET and ΣET distributions. Figures 2 and 3 compare the measured EF level transverse momentum distributions for empty bunch crossings and zero-bias events in data from runs in two different data-taking periods, F and G, with almost identical µ =7.0, before and after parameter h i changes were made. As mentioned above, calorimeter signals include effects of both in-time and out-of-time pileup. For calorimeter signals from bunch crossings in the middle of a bunch train, the average of positive energy signals and opposite-sign tails due to pileup roughly cancel. However, this cancellation does not occur for the first bunches in a train, which have fewer negative-signal tails contributing and therefore have a positive signal bias that increases as pileup becomes larger. The first bunches in a train therefore also miss have a larger fraction of events with high ET and ΣET. Figures 4 and 5 show the dependence of the miss ET and ΣET distributions on the bunch position in the train. The events in these figures were selected with a random trigger on filled bunch crossings. Distributions are compared for events with the same number of detected primary vertices, to reduce any differences due to different bunches in a train having

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miss different instantaneous luminosities. The increase in ET and ΣET for the first few bunches in a group are clearly visible in most of these figures. The simulation used here did not include the detailed bunch structure and its changes during the course of the 2011 data-taking period. For the reasons discussed above, the EF level energy determination is less sensitive than that of L1 to the various effects described. The tails of the simulated EF distributions are seen in Figure 1 to agree much better with the data than those of the L1 simulation. miss Figures 6 and 7 compare the ET and ΣET distributions of data events containing candidate W’s decaying leptonically with those of the corresponding simulated event samples. The selections used to miss obtain these events are described in Section 2. Note that, since muons are not included in ET and miss ΣET, the electron and muon distributions should be different. Much of the ET here is due to neutrinos miss escaping the detector rather than from resolution effects. Simulated ET distributions agree well with miss the measured ones. QCD background contributes to the excess in electron-decay data events at low ET . miss As is the case for zero-bias events, the data have a longer ΣET tail. The ET peak at about 40 GeV for W eν events, as compared with the steeply falling distribution for zero-bias events shown in Figure 1, → miss is a good illustration of the type of event feature that makes the ET trigger useful for selecting events with real missing transverse momentum. miss That the cause of non-zero ET in the bulk of events is due to fluctuations in calorimeter measure-

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0 20 40 60 80 100 120 0 100 200 300 400 500 600 700 miss EF ∑ E [GeV] EF ET [GeV] T

miss Figure 4: L1 (top) and EF (bottom) ET (left) and ΣET (right) distributions for events triggered on random colliding bunches. Events are selected by requiring 4 primary vertices detected by the tracking system. Distributions are compared for events in the ﬁrst 3 bunches of a train (line) and events in all other bunches (shaded).

miss ment of transverse momentum can be seen by looking at the event-by-event correlation between ET miss √ and ΣET. Figure 8 shows the x and y components of ET at L1 and EF plotted as a function of ΣET miss for zero-bias events, which should have little real ET . As shown in Figure 9, for narrow ranges of miss ΣET the central part of the ET distribution is approximately Gaussian. Figure 10 shows the standard miss deviation of E and Ey as a function of √ΣE . For the same ΣE , the E resolution at the EF level is 6 x 6 T T T seen to be much better than that at L1. The approximately linear dependence illustrated in these figures miss allows simple parameterization of the ET component resolution as a function of ΣET by fitting it to a function of the form a + b √ΣET, where a and b are defined so that the resolution has dimensions of energy. Although a quadratic function would better fit the L1 data, no advantage was found to doing so miss for trigger purposes. Note that for the ATLAS offline ET analysis [10, 11], which focused on events with particles escaping the detector, it was found sufficient to use a single constant in a parameterization √ miss miss of the form k ΣET. The ET significance, XS, is then defined as the dimensionless ratio of ET to miss this resolution. Triggering on XS allows selection of events whose ET is unlikely to have arisen from overall calorimeter energy measurement fluctuation. As shown in Section 5 below, since it takes the fluctuations from ΣET into account, the XS trigger rate is also much less sensitive to pileup effects than miss the ET triggers. In order to prevent artificially large or small values of XS arising from small energy deposits or

6 Bunch Xing # in train ≤ 3 Bunch Xing # in train ≤ 3

-1 10 Bunch Xing # in train > 3 10-1 Bunch Xing # in train > 3 ATLAS Preliminary ATLAS Preliminary s = 7 TeV s = 7 TeV -2 -2 Fraction of events 10 Fraction of events 10 No. of primary vertices = 10 No. of primary vertices = 10

-3 10 10-3

10-4 10-4

10-5 10-5

10-6 10-6 0 20 40 60 80 100 120 0 100 200 300 400 500 600 700 miss L1 ∑ E [GeV] L1 ET [GeV] T

≤ ≤ Bunch Xing # in train 3 10-1 Bunch Xing # in train 3 -1 10 Bunch Xing # in train > 3 Bunch Xing # in train > 3

ATLAS Preliminary ATLAS Preliminary 10-2 10-2 s = 7 TeV s = 7 TeV Fraction of events Fraction of events No. of primary vertices = 10 No. of primary vertices = 10

-3 -3 10 10

-4 10-4 10

-5 10-5 10

10-6 10-6 0 20 40 60 80 100 120 0 100 200 300 400 500 600 700 miss EF ∑ E [GeV] EF ET [GeV] T

miss Figure 5: L1 (top) and EF (bottom) ET (left) and ΣET (right) distributions for events triggered on random colliding bunches. Events are selected by requiring 10 primary vertices detected by the tracking system. Distributions are compared for events in the first 3 bunches of a train (line) and events in all other bunches (shaded). energy overflows it was found useful to implement several additional criteria in the XS trigger decision. miss Regardless of the calculated XS value, minimum values of ET (typically 10 GeV) and minimum and maximum values of ΣET (typically about 16 GeV and 4 TeV respectively) are imposed for an event to pass an XS trigger. At L1, events automatically pass the XS trigger if there is an overflow in the sums that give Ex or Ey, and automatically fail if there is an overflow in ΣET. Finally, to preserve efficiency for miss6 6 miss large ET , an event automatically passes the XS trigger if ET is greater than some value, typically set 10 or 20 GeV higher than the lowest threshold unprescaled XE trigger. These settings, which preserve efficiency and control the rate of false triggers, result in cutoffs in some of the distributions shown in the figures below. Figure 11 shows the distribution of XS at L1 and EF for events selected with a trigger firing on random bunch crossings and compares them with simulated minimum-bias events. The agreement is miss reasonable, with differences arising from the ET and ΣET differences seen in Figure 1. Figure 12 compares the XS distributions for runs in two periods with different EF level characterizations of pulse miss shape and σcell as described above. Some differences are visible, as would be expected from the ET and ΣET behavior shown in Figure 3. Figures 13 and 14 compare the XS distribution at L1 and EF for simulated W eν and W → → µν events with the candidate data events selected as described above. Agreement between data and

7 ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 6 6 10 10

5 5 10 10 Data 2011 Data 2011 Events/2 GeV Events/10 GeV 104 MC W → e ν 104 MC W → e ν

3 3 10 10

102 102

10 10

1 1 0 20 40 60 80 100 120 140 160 180 200 0 200 400 600 800 1000 1200 1400 miss L1 ∑ E [GeV] L1 ET [GeV] T

ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 6 6 10 10

5 5 10 10 Data 2011 Data 2011 Events/2 GeV Events/10 GeV → ν 4 → ν 104 MC W e 10 MC W e

3 3 10 10

2 102 10

10 10

1 1 0 20 40 60 80 100 120 140 160 180 200 0 200 400 600 800 1000 1200 1400 miss EF ∑ E [GeV] EF ET [GeV] T

miss miss Figure 6: Level 1 ET (top left), L1 ΣET (top right), EF level ET (bottom left) and EF ΣET (bottom right) distributions for candidate W eν events compared with expectations from simulation. →

miss simulation, for these events in which ET arises from true event characteristics rather than ﬂuctuations, is quite good, though not perfect. QCD background contributes to the excess in electron-decay data events at low XS. miss The XS value is an indication of how likely it is for the ET in an event to arise from the imperfect measurement resolution of the total energy deposited in the calorimeter in that event. However, the approximation of a single Gaussian behavior for distributions such as those in Figure 9 is only appropriate for the central region of these plots, for which XS is low. For example, most of the transverse energy in QCD two-jet events is likely to be localized in two back-to-back regions of the calorimeter, and jet- energy resolution will give rise to large XS more frequently than the Gaussian √ΣET model would predict. Therefore, XS alone cannot easily be used to separate such events from signal events containing miss true ET . As a result, while triggers with low XS thresholds are useful in event selection to enhance the signal to background fraction, high-XS-threshold triggers do not provide similar advantages. miss The standalone transverse-momentum triggers are those which accepted events solely based on ET , ΣET, or XS passing some threshold. The main standalone triggers used in 2011 are listed in Tables 1, 2 miss and 3. A large range of thresholds were used to insure that, regardless of beam luminosity, some ET and ΣET triggers could always run unprescaled. As discussed in the previous paragraph, it was not useful to set XS-trigger thresholds to high values, and these triggers almost always had to be prescaled. Except for signatures using the L2 FEB algorithm (discussed below) the L2 and L1 algorithms were almost identical, so typically the thresholds were set to the same value. However, because of the limited available number of L1 ﬁrmware thresholds, L2 thresholds were sometimes varied to allow more intermediate threshold values or to reduce rates when the highest L1 threshold was used. A number of combined triggers, which put requirements on both transverse-momentum and other event characteristics, were also used in 2011.

8 ATLAS Preliminary ∫ L dt = 4.3 fb-1, s = 7 TeV ATLAS Preliminary ∫ L dt = 4.3 fb-1, s = 7 TeV 106 106 Events / GeV Events / GeV 105 Data 2011 Data 2011 MC W → µ ν MC W → µ ν 104

105 103

102

104 10 0 5 10 15 20 25 30 35 40 0 100 200 300 400 500 600 700 L1 Emiss [GeV] L1 ∑ E [GeV] T T

ATLAS Preliminary ∫ L dt = 4.3 fb-1, s = 7 TeV ATLAS Preliminary ∫ L dt = 4.3 fb-1, s = 7 TeV 106 106

Events / GeV Events / GeV 5 Data 2011 10 Data 2011 MC W → µ ν MC W → µ ν 104 105 103

102 0 5 10 15 20 25 30 35 40 0 100 200 300 400 500 600 700 EF Emiss [GeV] EF ∑ E [GeV] T T

miss miss Figure 7: Level 1 ET (top left), L1 ΣET (top right), EF level ET (bottom left) and EF ΣET (bottom right) distributions for candidate W µν events compared with expectations from simulation. The → miss transverse momentum of muons is not included in these determinations of ET and ΣET.

For example, a W trigger using electrons can use a lower electron transverse-momentum threshold when it is combined with an XS requirement.

Signature Thresholds [GeV] Comments L1 L2 EF xe20 10 10 20 Prescaled xe30 20 20 30 Prescaled xe40 30 30 40 Prescaled xe50 35 35 50 Prescaled xe60 40 40 60 Prescaled only at high luminosity xe70 50 50 70 Prescaled only at high luminosity xe70 tight 60 60 70 Not prescaled xe80 60 60 80 Not prescaled xe90 60 70 90 Not prescaled

miss Table 1: Deﬁnition of the main standalone ET trigger signatures used in 2011. The suﬃx “tight” indicates that the lower level thresholds were higher than the nominal ones for the same EF level threshold.

9 100 106 100 106 80 ATLAS Preliminary 80 ATLAS Preliminary

[GeV] 5 [GeV] 5 x s = 7 TeV 10 y s = 7 TeV 10 E 60 E 60

L1 40 L1 40 104 104 20 20 0 103 0 103 -20 -20 2 2 -40 10 -40 10 -60 -60 10 10 -80 -80 -100 1 -100 1 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Σ 1/2 Σ 1/2 L1 ET [GeV ] L1 ET [GeV ]

100 100 105 105 80 ATLAS Preliminary 80 ATLAS Preliminary

[GeV] s = 7 TeV [GeV] x y s = 7 TeV

E 60 E 60 104 104

EF 40 EF 40 20 20 103 103 0 0

-20 102 -20 102 -40 -40 -60 10 -60 10 -80 -80 -100 1 -100 1 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Σ 1/2 Σ 1/2 EF ET [GeV ] EF ET [GeV ]

Figure 8: Level 1 E (top left), L1 Ey (top right), EF level E (bottom left) and EF Ey (bottom right) 6 x 6 6 x 6 plotted versus the respective level ΣET for random triggers on colliding bunches.

Signature Thresholds [GeV] Comments L1 L2 EF te550 180 250 550 Prescaled 300 350 550 Prescaled; settings used at high luminosity te700 300 350 700 Not prescaled; settings in very early data collection period 300 300 700 Prescaled; settings used most of 2011 500 500 700 Prescaled; settings used at high luminosity te900 500 500 900 Not prescaled; settings in very early data collection period 400 400 900 Prescaled; settings used most of 2011 700 700 900 Prescaled; settings used at high luminosity te1000 500 500 1000 Not prescaled; settings used most of 2011 800 800 1000 Not prescaled; settings used at high luminosity te1100 600 600 1100 Not prescaled; settings used much of 2011 500 600 1100 Not prescaled; settings used in later part of 2011 800 900 1100 Not prescaled; settings used at high luminosity te1200 700 700 1200 Not prescaled; settings used much of 2011 500 700 1200 Not prescaled; settings used in later part of 2011 800 1000 1200 Not prescaled; settings used at high luminosity

Table 2: Definition of the standalone ΣET trigger signatures used in 2011. For each signature, Leve1 1 and Level 2 thresholds varied during 2011 as specified in the comments, but only one configuration was active for each signature at a given time.

10 105 102 σ = 4.17 ± 0.01 ATLAS Preliminary Sigma = 16.71 ± 1.76 ATLAS Preliminary Σ ≤ 104 5 < ET 5.25 s = 7 TeV Σ ≤ s = 7 TeV 17.5 < ET 17.75

Events/GeV 103 Events/GeV 10

102

10 1

-1 -1 10-50 -40 -30 -20 -10 0 10 20 30 40 50 10-50 -40 -30 -20 -10 0 10 20 30 40 50

L1 Ex [GeV] L1 Ex [GeV]

105 104 σ = 1.964 ± 0.003 ATLAS Preliminary σ = 8.084 ± 0.041 ATLAS Preliminary 104 5 < Σ E ≤ 5.25 s = 7 TeV 17.5 < Σ E ≤ 17.75 s = 7 TeV T 103 T

Events/GeV 103 Events/GeV 102 102 10 10

1 1

-1 -1 10-50 -40 -30 -20 -10 0 10 20 30 40 50 10-50 -40 -30 -20 -10 0 10 20 30 40 50

EF Ex [GeV] EF Ex [GeV]

Figure 9: E distributions for Level 1 (top) and EF level (bottom) as determined from the sum over the 6 x full set of calorimeter trigger towers (for Level 1) or calorimeter cells (for EF level) for events selected with a random trigger on colliding bunches. These are shown for two different calorimeter ΣET ranges, and are compared with Gaussian fits to the distributions. The results from these fits to the peak region miss data points (with statistical errors as shown in the figure) are used to determine the event-by-event ET expected from calorimeter energy measurement fluctuations.

Signature Thresholds Comments L1 L2 EF xs30 1.5 1.5 3.0 Prescaled. In later periods used L1 XE10 instead of L1 XS15. xs45 3.0 3.0 4.5 Prescaled xs60 4.5 4.5 6.0 Prescaled xs75 5.0 5.0 7.5 Prescaled xs100 6.0 6.0 10.0 Unprescaled at low luminosity, prescaled at high luminosity

Table 3: Deﬁnition of the standalone XS trigger signatures used in 2011.

11 35 35 χ2 / ndf 3426 / 60 χ2 / ndf 3081 / 60

[GeV] 30 [GeV] 30 ± y ± x Offset -1.792 ± 0.005 Offset -1.787 0.005 σ Slope 1.169 ± 0.001 σ Slope 1.156 ± 0.001

L1 25 L1 25 ATLAS Preliminary ATLAS Preliminary 20 s = 7 TeV 20 s = 7 TeV

15 15

10 10

5 5

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Σ 1/2 Σ 1/2 L1 ET [GeV ] L1 ET [GeV ] 35 35 χ2 / ndf 207.3 / 81 χ2 / ndf 371.6 / 81

[Gev] 30 [Gev] 30 x Offset -0.5493 ± 0.0022 y Offset -0.6035 ± 0.0022 σ σ Slope 0.4918 ± 0.0003 Slope 0.5044 ± 0.0003

EF 25 EF 25 ATLAS Preliminary ATLAS Preliminary 20 s = 7 TeV 20 s = 7 TeV

15 15

10 10

5 5

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Σ 1/2 Σ 1/2 EF ET [GeV ] EF ET [GeV ]

Figure 10: Standard deviation of E (left) and Ey (right) for L1 (top) and EF (right) as determined from 6 x 6 the sum over the full set of calorimeter trigger towers (for Level 1) or calorimeter cells (for EF level) for events selected with a random trigger on colliding bunches. A linear fit to the standard deviation as miss a function of the square root of the total calorimeter ΣET is used to determine the event-by-event ET expected from calorimeter energy measurement fluctuations. The error bars are the statistical errors on the standard deviation determined from a Gaussian fit to the individual E and Ey distributions for each 6 x 6 ΣET bin. The non-linearity at Level 1 means that fewer events than predicted by the line will fluctuate above any given E or Ey value. 6 x 6

106 106 ATLAS Preliminary Data 2011 ATLAS Preliminary Data 2011 Events 5 Events 10 s = 7 TeV 5 s = 7 TeV MC minbias 10 MC minbias 104 104

3 10 103

2 10 102

10 10

1 1 0 5 10 15 20 25 0 5 10 15 20 25 L1 XS EF XS

Figure 11: Level 1 (left) and EF level (right) XS distributions for events selected with a random trigger on colliding bunches compared with expectations from simulation.

12 10-1

ATLAS Preliminary Run from period F s = 7 TeV Run from period G 10-2 Fraction of events

10-3

10-4

0 1 2 3 4 5 6 7 8 EF XS

Figure 12: EF level XS distributions for events selected with a random trigger on colliding bunches compared for data recorded in two periods, both with µ =7.0 but using diﬀerent deﬁnitions of noise h i widths for zero suppression.

ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 6 6 10 10 Events Events

5 5 10 10 Data 2011 Data 2011

4 → ν → ν 10 MC W e 104 MC W e

3 3 10 10

2 10 2 10

10 10

1 1 0 5 10 15 20 25 0 5 10 15 20 25 L1 XS EF XS

Figure 13: Level 1 (left) and EF level (right) XS distributions for simulated W eν events compared → with data.

6 -1 -1 10 ATLAS Preliminary ∫ L dt = 4.3 fb , s = 7 TeV 106 ATLAS Preliminary ∫ L dt = 4.3 fb , s = 7 TeV Events Events 105 105

4 104 Data 2011 10 Data 2011 MC W → µ ν MC W → µ ν 3 103 10

2 2 10 10 10 10 1 1 0 5 10 15 20 25 0 5 10 15 20 25 L1 XS EF XS

Figure 14: Level 1 (left) and EF level (right) XS distributions for simulated W µν events compared → with data. The transverse momentum of muons is not included in these determinations of XS.

13 4 Comparison of trigger and oﬄine measurements

In general, the offline analysis uses more sophisticated algorithms than are possible to implement at trigger level. The degree to which the trigger level transverse momentum quantities reproduce offline ones [10, 11] is a measure of how effective these triggers are in selecting events which would be used in analysis while rejecting those that will be thrown out. As discussed in the previous section, the 2011 trigger- level determinations of transverse momentum used only the calorimeter and did not include hadronic calibration. The offline determination chosen for comparing with the trigger is therefore one using the calorimeter only, and no hadronic calibration. The cluster algorithm it uses provides a determination of transverse momentum which is closer than that of the trigger to the best offline determination. miss Figure 15 compares the trigger and offline measurements of ET and ΣET for events obtained with miss miss a random trigger. The correlation is very poor for L1 ET , since in these events ET is mainly due to energy mismeasurement, which is different in the L1 trigger-tower algorithm from that used offline. Correlation between L1 and offline measurements can more easily be seen for the larger valued ΣET. The EF level measured quantities, on the other hand, show strong correlation with offline values. The EF level ΣET is offset at low energies from the offline ΣET, by about 20 GeV for the run shown in these plots. This is mainly due to the one-sided noise cut used at EF level, which adds an offset compared with the offline two-sided cut.

40 300 ATLAS Preliminary 35 ATLAS Preliminary 250 103 3 L1 [GeV] s= 7 TeV L1 [GeV]

10 T

30 E s= 7 TeV miss T Σ E 200 25 2 2 10 20 10 150

15 100 10 10 10 50 5

0 0 0 5 10 15 20 25 30 35 40 1 0 100 200 300 400 500 600 1 miss ΣE (offline, EM scale) [GeV] ET (offline, EM scale) [GeV] T

40 600 103 35 ATLAS Preliminary 103 ATLAS Preliminary 500 EF [GeV] EF [GeV] 30 s= 7 TeV T s= 7 TeV E miss T Σ E 400 25 102 102 20 300

15 200 10 10 10 100 5

0 1 0 0 5 10 15 20 25 30 35 40 0 100 200 300 400 500 600 1 miss ΣE (offline, EM scale) [GeV] ET (offline, EM scale) [GeV] T

miss Figure 15: Level 1 (top) and EF Level (bottom) ET (left) and ΣET (right) compared with the oﬄine calculated values for events collected with a trigger ﬁring on random bunch crossings for run 183081 with peak µ = 6.9.

miss The trigger behavior for events with real ET is studied using the W samples obtained as described in Section 2. Figure 16 compares the trigger and oﬄine measurements of Emiss and ΣE for W eν T T → candidate events. Figure 17 compares the trigger and oﬄine measurements of Emiss and ΣE for W µν T T → candidate events. For all of these events, the transverse momentum quantities are likely dominated by

14 true values larger than the fluctuations. The EF quantities still show better correlation with the offline variables than do the L1 ones, but even the L1 ones show good correlation for these events. The EF level ΣET offset from offline at low offline ΣET visible in these plots arises from a complex combination of the event selection cuts and kinematics, in addition to the cell-energy cut effects described for zero-bias events.

200 400 -1 -1

ATLAS Preliminary, ∫ L dt = 4.7 fb , s = 7 TeV 4 [GeV] ATLAS Preliminary, ∫ L dt = 4.7 fb , s = 7 TeV

180 T 10 350 [GeV]

E 3 10 160 ∑ miss T

L1 300

140 3

L1 E 10 250 120 102 100 200 102 80 150 60 10 100 10 40 50 20

0 0 0 20 40 60 80 100 120 140 160 180 200 1 0 50 100 150 200 250 300 350 400 1 miss (offline, EM scale) E [GeV] (offline, EM scale) ∑ ET [GeV] T

200 400

-1 -1 3 180 ATLAS Preliminary, ∫ L dt = 4.7 fb , s = 7 TeV ATLAS Preliminary, ∫ L dt = 4.7 fb , s = 7 TeV 10 4 350 [GeV] 10 [GeV] T 160 E miss T 300 ∑ 140 3

EF E 10 EF 250 2 120 10

100 200 102 80 150 60 10 100 40 10 50 20

0 0 0 20 40 60 80 100 120 140 160 180 200 1 0 50 100 150 200 250 300 350 400 1 miss (offline, EM scale) E [GeV] (offline, EM scale) ∑ ET [GeV] T

miss Figure 16: Level 1 (top) and EF Level (bottom) ET (left) and ΣET (right) compared with the oﬄine calculated values for W eν candidate events. →

15 100 600 105 ATLAS Preliminary ∫ L dt = 4.3 fb-1, s = 7 TeV ATLAS Preliminary ∫ L dt = 4.3 fb-1, s = 7 TeV 90 104 [GeV] [GeV]

T 500

80 4 E miss T 10 ∑ 70 3 L1 L1 E 400 10 60 103 50 300 102 40 102 200 30 20 10 10 100 10 0 1 0 1 0 10 20 30 40 50 60 70 80 90 100 0 100 200 300 400 500 600 (offline, EM scale) Emiss [GeV] (offline, EM scale) ∑ E [GeV] T T

100 5 600 4 -1 10 -1 10 90 ATLAS Preliminary ∫ L dt = 4.3 fb , s = 7 TeV ATLAS Preliminary ∫ L dt = 4.3 fb , s = 7 TeV [GeV] [GeV]

T 500

80 4 E miss T 10

∑ 3 70 10 400 EF E EF 60 103

50 300 2 10 40 102 200 30 10 20 10 100 10 0 1 0 1 0 10 20 30 40 50 60 70 80 90 100 0 100 200 300 400 500 600 (offline, EM scale) Emiss [GeV] (offline, EM scale) ∑ E [GeV] T T

miss Figure 17: Level 1 (top) and EF Level (bottom) ET (left) and ΣET (right) compared with the oﬄine calculated values for candidate W µν events. The transverse momentum of muons is not included in miss → these determinations of ET and ΣET.

5 Stability of the triggers and the impact of pileup

At high luminosities there are multiple proton-proton interactions in a single bunch crossing. Figure 18 shows the development in 2011 of the number of interactions per bunch crossing at the LHC. The maximum value of µ in a day increased from an initial value of about 3 to a typical value of about 10 to 15 and as high as 30 for one special run (not shown in this plot). As µ increases, so does the average energy deposited in the calorimeter. This results in a shift in the ΣET distribution, as shown in the left panel of Figure 19. Since the ΣET distribution is roughly a falling exponential, the rates of TE triggers, which fire when ΣET is above some threshold, increase much more quickly than linearly with increasing µ (Figure 19 right). Since TE triggers are very sensitive to pileup, they were used in 2011 primarily to provide an unbiased Level 1 trigger for heavy ion collisions, by setting the threshold to a very low value. miss miss For low to moderate ET values, the bulk of ET triggers are due to calorimeter measurement miss miss fluctuations in events without real ET . As ΣET increases with pileup, the ET resolution function √ miss broadens in proportion to ΣET. ET therefore becomes larger with increasing µ (Figure 20 left) and miss the ET trigger rates grow much more quickly than linearly with µ (Figure 20 top right). On the other hand, for high thresholds other processes, such as mismeasurement of jet energies in QCD two-jet events, become more important than resolution in determining the trigger rate. As Figure 20 bottom right shows, for such thresholds the trigger rates are linear with µ. As discussed in Section 3, changes in the LHC such as in bunch structure configuration result in differences in calorimeter response, so that trigger rates per bunch crossing are not identical at different

16 Figure 18: The maximum mean number of events per beam crossing versus day. The online luminosity measurement is used for this calculation. Only the maximum value during stable beam periods is shown. In this plot both the maximum pileup for any bunch is shown in green, as well as the maximum pileup averaged over all the colliding bunches (shown in blue).

10-1 -1 700 GeV ATLAS Preliminary µ = 4 10 900 GeV µ = 6 -2 s = 7 TeV 1000 GeV 10 µ = 8 10-2 1100 GeV µ = 10 1200 GeV 10-3 µ = 12 -3 Fraction of events µ = 14 10 µ = 16 10-4 10-4 10-5 10-5 10-6 s = 7 TeV (2011)

Unprescaled rate / colliding bunch [Hz] ATLAS Preliminary 10-6 0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 µ EF Y ET [GeV]

Figure 19: The ﬁgure on the left shows EF level ΣET distributions for various values of the average number of interactions per bunch crossing µ for a random trigger on colliding bunches. The ﬁgure on the right shows the rates of ΣET triggers with thresholds of 700, 900, 1000, 1100, and 1200 GeV (corrected for prescales used) for data recorded from 13 July to 30 October 2011 as a function of the number of interactions per bunch crossing. Each dot represents an average over about 8 minutes of data.

miss periods even for bunches with the same µ. The low to moderate ET threshold rates are particularly sensitive to beam conditions and detector eﬀects (such as noisy cells), so, as seen in Figure 20, there are miss large variations in ET rate for the same µ. This can be seen more clearly in Figure 21, which shows that while in general the rates versus µ lie along a single curve, there are discontinuities in rates for some run periods. As seen in these ﬁgures, this is less true for high threshold triggers. Since most of the pileup energy is deposited at a small angle from the collision axis, pileup particularly impacts the forward region of the calorimeter. Increasing the noise widths σcell for zero-suppression in this part of the calorimeter was found to be helpful in controlling trigger rates. Figure 22 compares the trigger rates as a function of µ for data recorded before and after including pileup in the noise cuts. For the same µ, there is a reduction in rate by over a factor of 3 for the 20 GeV threshold trigger, and by about a third for one with a threshold of 80 GeV. As mentioned above, the thresholds were changed once

17 ATLAS Preliminary 102 s = 7 TeV (2011)

1 10-1 ATLAS Preliminary µ = 4 µ = 6 10-1 20 GeV -2 s = 7 TeV 10 µ = 8 30 GeV µ = 10 40 GeV Unprescaled rate / colliding bunch [Hz] 10-3 µ = 12 10-2 µ 0 5 10 15 20 Fraction of events = 14 µ µ 10-4 = 16 0.01 ATLAS Preliminary 10-5 s = 7 TeV (2011) 0.008 10-6 60 GeV 70 GeV 0 10 20 30 40 50 0.006 80 GeV miss 90 GeV EF ET [GeV] 0.004

0.002 Unprescaled rate / colliding bunch [Hz] 0 5 10 15 20 µ

miss Figure 20: The figure on the left shows EF level ET distributions for various values of the average number of interactions per bunch crossing µ for a random trigger on colliding bunches. The figures on miss the right show how the rates per bunch crossing (corrected for prescales used) of ET triggers change miss as a function of µ. The top right figure shows the rates of ET triggers with thresholds of 20, 30 and 40 GeV for data recorded from 14 April to 30 October 2011. The bottom right figure shows the rates of miss ET triggers with thresholds of 60, 70, 80 and 90 GeV for data recorded from 13 July to 30 October 2011. Each dot represents an average over about 8 minutes of data. The earlier period data uses different zero suppression, but was included in the top plot because the 30 GeV threshold trigger was turned off afterwards. at EF level during 2011, but were kept fixed at L1. While increasing the value of the forward calorimeter miss cutoff for zero-suppression led to improvements in rate without severely affecting ET resolution, stud- miss ies showed that completely eliminating the forward region of the calorimeter from the ET calculation at either L1 or EF would result in poorer agreement with the offline value. The trigger therefore always used the full calorimeter. miss To the extent that the XS triggers correctly model the ET resolution, the XS trigger rate per bunch miss crossing for events with ET arising from calorimeter mismeasurements should be independent of µ. However, changes in bunch structure or other variations can change XS behavior just as they do that of XE triggers. To study these effects, XS parameters are separately extracted for several runs, using the fitting method described in Section 3 and shown in Figure 10 for the data recorded in periods G through M. The properties of the individual runs used here are listed in Table 4. These runs vary in the average number of events per bunch crossing, the time between consecutive filled bunches, and in whether cell miss zero suppression and calorimeter pulse shapes were tuned for higher pileup. Table 5 presents the ET resolution parameters obtained from the fits. The two fit parameters are strongly anti-correlated, with correlation coefficients ranging from -0.94 to -0.99, so for comparison between periods with different conditions it is useful to determine the resulting resolution at a few values of √ΣET. Table 6 lists the

18 ATLAS Preliminary 102 2011 G s = 7 TeV 2011 H 2011 I 10 2011 J 20 GeV 2011 K 1 2011 L 2011 M 10-1 40 GeV 10-2 70 GeV 10-3 Unprescaled rate / colliding bunch [Hz] 0 5 10 15 20 µ

miss Figure 21: Comparison of ET trigger rates for data-taking periods G through M (27 May to 30 October 2011, shown in different colors). Rates (corrected for prescales used) as a function of the number of miss interactions per bunch crossing µ are shown for ET triggers with thresholds of 20, 40 and 70 GeV. No systematic differences arise between periods from variations in detector or beam conditions. Within some of the periods, however, for which overall detector and beam settings are expected to be stable, different rates are seen for the same threshold and value of µ. Each dot represents an average over about 8 minutes of data.

102 20 GeV, E & F 10 20 GeV, G & H 80 GeV, E & F 1 80 GeV, G & H

10-1

10-2

-3 10 s = 7 TeV (2011)

Unprescaled rate / colliding bunch [Hz] ATLAS Preliminary 10-4 0 2 4 6 8 10 12 14 µ

miss Figure 22: Comparison of ET trigger rates (corrected for prescales used) as a function of µ for data- taking periods E and F, with the rates for periods G and H. For the latter periods, the cell signal parameterization and noise model included pileup eﬀects. Each dot represents an average over about 8 minutes of data.

miss calculated ET resolutions at ΣET=16 GeV, the minimum ΣET used in the fits and required for events to pass XS, and 125 GeV, a middle range of ΣET for data used in the fits. The uncertainties in this table are determined by propagating errors using the covariance matrix of each fit. Several conclusions can be drawn from the results in Table 6. The L1 resolutions all agree to about 5%. The E and Ey and run-to-run variations are all at about this level, so it is difficult to make any 6 x 6 conclusions beyond this regarding L1. The L1 resolutions are significantly worse than those at EF, which is expected given the finer spatial binning and better energy resolution at EF.

19 Run Peak Bunch Increased Zero Run Number Period µ Spacing Suppression 177986 B 5.7 75 ns No 178044 B 8.3 75 ns No 182424 F 6.2 50 ns No 182486 F 7.3 50 ns No 183081 G 6.9 50 ns Yes 183130 G 5.0 50 ns Yes 190256 L 15.6 50 ns Yes 191190 M 16.7 50 ns Yes

Table 4: Characteristics of data runs used in XS parameter ﬁtting.

Component L1 Fit Parameters EF Fit Parameters Run Number a [GeV] b [GeV0.5] a [GeV] b [GeV0.5] 177986 E 2.172 0.260 1.213 0.055 0.776 0.036 0.428 0.005 6 x − ± ± − ± ± Ey 1.778 0.248 1.104 0.053 0.666 0.040 0.416 0.005 6 − ± ± − ± ± 178044 E 1.707 0.061 1.143 0.012 0.723 0.015 0.428 0.002 6 x − ± ± − ± ± Ey 1.534 0.059 1.081 0.012 0.733 0.015 0.430 0.002 6 − ± ± − ± ± 182424 E 1.718 0.068 1.149 0.014 0.713 0.016 0.422 0.002 6 x − ± ± − ± ± Ey 1.719 0.068 1.119 0.014 0.726 0.016 0.423 0.002 6 − ± ± − ± ± 182486 E 1.676 0.061 1.132 0.012 0.748 0.022 0.425 0.002 6 x − ± ± − ± ± Ey 1.608 0.060 1.101 0.012 0.749 0.023 0.426 0.002 6 − ± ± − ± ± 183081 E 1.624 0.053 1.130 0.011 0.609 0.014 0.502 0.002 6 x − ± ± − ± ± Ey 1.602 0.052 1.094 0.011 0.577 0.015 0.500 0.002 6 − ± ± − ± ± 183130 E 1.665 0.085 1.139 0.018 0.595 0.020 0.501 0.003 6 x − ± ± − ± ± Ey 1.581 0.083 1.077 0.017 0.597 0.020 0.504 0.003 6 − ± ± − ± ± 190256 E 1.997 0.050 1.185 0.008 0.554 0.022 0.481 0.002 6 x − ± ± − ± ± Ey 1.855 0.040 1.152 0.008 0.551 0.022 0.482 0.002 6 − ± ± − ± ± 191190 E 1.953 0.037 1.183 0.007 0.606 0.022 0.487 0.002 6 x − ± ± − ± ± Ey 1.876 0.037 1.156 0.007 0.522 0.023 0.480 0.002 6 − ± ± − ± ± Table 5: L1 and EF XS parameterization extracted from runs with diﬀerent characteristics.

For both trigger levels, resolution at low ΣET values is better than what would be expected from a straight line fit to high ΣET values constrained to go through the origin, demonstrating the need for a non-zero constant offset a in the fit to trigger data. It is likely that this is because at low ΣET the energy comes mainly from the fluctuations in the large number of cells remaining after zero suppression, so that the direction-weighted sum of these energies cancels out to a large degree. On the other hand, for high ΣET energy is typically deposited by particles, so it is distributed in fewer cells and measurement miss fluctuations are more likely to result in measured ET . In fact, the EF fit predicted resolution of about miss 1 GeV at ΣET of 16 GeV for period F matches well the 1.2 GeV ET peak in period F data for empty bunch crossings shown Figure 1, for which ΣET has a peak at about 17 GeV. The resolutions for runs with identical conditions are as consistent as their own E and Ey differences 6 x 6 at both trigger levels. For Level 1, the resolutions in the two runs with 75 ns bunch spacing are roughly consistent with each other and with the 50 ns bunch spacing runs. At EF Level, the resolutions in the 75 ns runs are consistent with those of the early 50 ns runs which had the same zero-suppression settings. At EF Level, for which zero-suppression settings were modified once during 2011, there is a significant change in the E and Ey resolution dependence on ΣE after the implementation of increased zero 6 x 6 T

20 Component L1 Resolution [GeV] EF Resolution [GeV] Run Number ΣET=16 GeV ΣET=125 GeV ΣET=16 GeV ΣET=125 GeV 177986 E 2.68 0.05 11.39 0.36 0.94 0.02 4.02 0.03 6 x ± ± ± ± Ey 2.64 0.05 10.56 0.35 1.00 0.02 3.99 0.03 6 ± ± ± ± 178044 E 2.87 0.02 11.07 0.08 0.99 0.01 4.06 0.01 6 x ± ± ± ± Ey 2.79 0.02 10.55 0.07 0.99 0.01 4.07 0.01 6 ± ± ± ± 182424 E 2.88 0.02 11.12 0.09 0.98 0.01 4.01 0.01 6 x ± ± ± ± Ey 2.76 0.02 10.80 0.09 0.97 0.01 4.00 0.01 6 ± ± ± ± 182486 E 2.85 0.02 10.98 0.08 0.95 0.01 4.01 0.01 6 x ± ± ± ± Ey 2.80 0.01 10.70 0.08 0.96 0.01 4.01 0.01 6 ± ± ± ± 183081 E 2.90 0.01 11.01 0.07 1.40 0.01 5.00 0.01 6 x ± ± ± ± Ey 2.77 0.01 10.63 0.07 1.42 0.01 5.01 0.01 6 ± ± ± ± 183130 E 2.89 0.02 11.07 0.11 1.41 0.01 5.01 0.02 6 x ± ± ± ± Ey 2.73 0.02 10.46 0.11 1.42 0.01 5.04 0.02 6 ± ± ± ± 190256 E 2.74 0.01 11.25 0.05 1.37 0.01 4.82 0.01 6 x ± ± ± ± Ey 2.75 0.01 11.02 0.05 1.38 0.01 4.84 0.01 6 ± ± ± ± 191190 E 2.78 0.01 11.27 0.04 1.34 0.01 4.84 0.01 6 x ± ± ± ± Ey 2.75 0.01 11.05 0.04 1.40 0.01 4.84 0.01 6 ± ± ± ± Table 6: Calculated L1 and EF E and Ey resolution in GeV for various ΣE values using fits for different 6 x 6 T run periods. As discussed in the text, the zero-suppression was increased, at EF Level only, between runs 182486 and 183081. suppression. As seen in the right side of Figure 3, there was a large decrease in ΣET after the increase in zero suppression, with the peak of the distribution on random triggers dropping from about 135 GeV to about 65 GeV. The calculated resolution at the peak thus improves at EF level from about 4.2 GeV to about 2.8 GeV. As discussed above and shown in Figure 22 this was accompanied by a significant de- miss crease in the ET trigger rate, especially for low thresholds for which measurement fluctuations are the main source of triggers. On the other hand, the calculated resolution at the same value of ΣET increases after increased zero suppression. This is likely because with more randomly-distributed calorimeter noise removed the same ΣET must arise from events with more real energy deposit. With fewer cells contributing to ΣET there will be less directional cancellation and the resulting variation of the measured miss ET will be larger. After the increase in zero suppression at EF Level, resolutions remained mainly unchanged as a function of ΣET even when µ doubled, except for what appears to be a small statistically significant miss improvement in resolution for high ΣET values. The goal of a pileup-independent determination of ET fluctuations is thus largely achieved with this parameterization. As just discussed, for fixed conditions there was little change over time in measured resolution. Because of the need to quickly implement the trigger before a full, detailed study could be done, the XS trigger constants actually used in the trigger in 2011 were initially set to a = 1 and b = 1 for L1 − and L2, and a = 0.48 and b = 0.4 for EF. As it is undesirable to make frequent changes in trigger − settings, these parameters were changed only once in 2011, after increase in pileup and modification in EF zero-suppression settings, to a = 1.43 and b = 1.12 for L1 and L2 and a = 0.23 and b = 0.46 for − − EF. The resulting resolutions disagree by at most 15% from the values in Table 6. The µ dependence of XS is further studied in Figure 23. The left plot in this figure shows XS distributions for several values of µ. These appear almost unchanged even as µ changes by a factor of miss 4. On the other hand, as resolution becomes worse with increasing µ, the effective ET threshold for a miss miss fixed XS increases, so efficiency for events with true ET goes down. At high XS values, where ET

21 is dominated by sources other than ΣET measurement ﬂuctuations, the trigger rate can actually go down with pileup. These eﬀects can be seen in the right-side plot of Figure 23.

10-1 ATLAS Preliminary 2011 G ATLAS Preliminary µ = 4 102 s = 7 TeV 2011 H 10-2 s = 7 TeV µ = 6 µ = 8 2011 I = 10 10 3.0 2011 J -3 µ 10 µ = 12 2011 K 2011 L Fraction of events µ = 14 1 10-4 µ = 16 4.5 2011 M

10-1 10-5 6.0 10-2 10-6 7.5 Unprescaled rate / colliding bunch [Hz] 10-3 0 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 µ EF XS

Figure 23: The ﬁgure on the left shows the Event Filter level XS distributions for various values of the average number of interactions per bunch crossing µ for a random trigger on colliding bunches. The ﬁgure on the right shows the dependence on µ of rates per bunch crossing (corrected for prescales used) of XS triggers with thresholds of 3.0, 4.5, 6.0 and 7.5 for data recorded 27 May to 30 October 2011 Each dot represents an average over about 8 minutes of data.

As an illustration of how effects that can be removed offline must be dealt with by the trigger, note the excess of events at XS between 5 and 10 for µ = 8 in the left-side plot of Figure 23. Figure 24 shows the same plot after removing events identified offline as having calorimeter noise bursts or badly measured jets. Here the µ = 8 curve lies between those of higher and lower µ values, as expected.

10-1 ATLAS Preliminary µ = 4 µ 10-2 s = 7 TeV = 6 µ = 8 µ = 10 -3 10 µ = 12 µ Fraction of events = 14 10-4 µ = 16

10-5

10-6

0 1 2 3 4 5 6 7 8 9 10 EF XS

Figure 24: The Event Filter level XS distributions for various values of the average number of interactions per bunch crossing µ for a random trigger on colliding bunches. Events identiﬁed oﬄine as having calorimeter noise bursts or badly measured jets were removed from the data samples used.

The decision to use XE or XS triggers as a function of µ is therefore one of choosing between the limitations of each trigger: XE has close to constant eﬃciency at any threshold but the increase in rates with µ means that its threshold or prescale must be raised to maintain the same rate, while the XS threshold and prescale can be kept at the same values with increasing µ but its eﬃciency goes down as miss µ increases. In practice, the unprescaled chains for ET used in 2011 were of the XE type. The L1 and EF initial thresholds, initially set at 40 and 60 GeV respectively, had to be increased by about 10 GeV

22 as luminosity increased. Prescales of lower threshold XE signatures had to be increased as luminosity increased. The primary use of XS in 2011 was for combined triggers using transverse momentum in addition to other event properties, such as the presence of lepton candidates.

6 Trigger eﬃciency

As the amount of computing time and detector information available to calculate variables at various trigger levels is limited, the precision with which they are determined cannot match that of the offline calculation. The performance of the trigger is studied here by determining the fraction of events that pass a trigger threshold T on variable V as a function of offline value of V. A trigger perfectly duplicating the offline value would have zero efficiency for V < T and 100 % efficiency for V T. Resolution effects ≥ smear out this curve, and the bigger the spread between the trigger and offline variable, the slower the rise of this “turn-on curve”. As the efficiency depends on the nature of energy deposit in the calorimeter, the precise behavior may depend strongly on the particular events of interest. Here we study efficiencies for W decays since they provide a good example of events with non-interacting particles producing real miss ET . Figures 25 through 27 show the turn-on curves for various XE thresholds for candidate W eν → decay events compared with the simulated efficiency. The thresholds for each of these trigger signatures at the various trigger levels are given in Table 1. The EF level and combined curves agree to within a few GeV, showing that the various resolution effects are reasonably consistent with what is expected. The W L1 agreement is less good, especially near the bumps of about 40 GeV. These arise from the cut on mT , which is calculated from offline reconstructed quantities rather than the ones determined at trigger level. Figures 28 through 30 show the turn-on curves for various XS thresholds for candidate W eν → decay events compared with the simulated efficiency. The thresholds for each of these trigger signatures at the various trigger levels are given in Table 3. Since what is of interest in analysis is the dependence of miss miss efficiency on ET , the efficiency is presented as a function of offline ET rather than offline XS. As XS miss depends both on on ET and the less well-modeled ΣET distributions, the simulated XS turn-on curve agreement with data is somewhat worse than for XE. In particular, the larger high ΣET tail in data causes miss XS efficiency to be lower for any value of ET than would be expected from the simulation. Figure 31 shows the turn-on curves for various XE thresholds for candidate W µν decay events miss → compared with the simulated efficiency. As muons are not included in the ET calculation, the kinematics of these events at any value of Emiss is quite different than that of W eν events. T →

23 1 1

Efficiency 0.9 Efficiency 0.9

0.8 0.8

0.7 0.7

0.6 L1 XE10 0.6 L1 XE20

0.5 Data 2011 0.5 Data 2011 MC W → e ν MC W → e ν 0.4 ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 0.4 ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 220 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T

1 1

Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 L1 XE30 0.4 L1 XE35

1 1

Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 L1 XE40 0.4 L1 XE50

Data 2011 Data 2011 0.2 MC W → e ν 0.2 MC W → e ν ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 0 0 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 220 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T Figure 25: Comparison of measured and simulated Level 1 trigger efficiency for various XE triggers for W eν events. Because it involves a sum over the full calorimeter, the efficiency behavior may vary → miss significantly for different event samples. The structure near 40 GeV offline ET in some of these plots W arises from the cut on the mT used in selecting these events to reduce QCD background.

24 1 1 Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 EF XE20 0.4 EF XE30

1 1

Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 EF XE40 0.4 EF XE50

1 1 Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 EF XE60 0.4 EF XE70

Data 2011 Data 2011 0.2 MC W → e ν 0.2 MC W → e ν ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 0 0 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 220 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T Figure 26: Comparison of measured and simulated EF level trigger efficiency for various XE triggers for W eν events. Because it involves a sum over the full calorimeter, the efficiency behavior may vary → significantly for different event samples.

25 1 1 Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 L1 XE10 +EF XE20 0.4 L1 XE20 +EF XE30

1 1

Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 L1 XE30 +EF XE40 0.4 L1 XE35 +EF XE50

1 1 Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 L1 XE40 +EF XE60 0.4 L1 XE50 +EF XE70

Data 2011 Data 2011 0.2 MC W → e ν 0.2 MC W → e ν ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 0 0 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 220 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T Figure 27: Comparison of measured and simulated combined all-level trigger efficiency for various XE triggers for W eν events. Because it involves a sum over the full calorimeter, the efficiency behavior → may vary significantly for different event samples.

26 1 1

Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 L1 XS15 0.4 L1 XS30

1 1

Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 L1 XS45 0.4 L1 XS50

Data 2011 Data 2011 0.2 MC W → e ν 0.2 MC W → e ν ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 0 0 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 220 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T Figure 28: Comparison of measured and simulated Level 1 trigger efficiency for various XS triggers for W eν events. Because it involves a sum over the full calorimeter, the efficiency behavior may vary → miss significantly for different event samples. The structure near 40 GeV offline ET in some of these plots W arises from the cut on the mT used in selecting these events to reduce QCD background.

27 1 1

Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 EF XS30 0.4 EF XS45

1 1

Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 EF XS60 0.4 EF XS75

Data 2011 Data 2011 0.2 MC W → e ν 0.2 MC W → e ν ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 0 0 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 220 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T Figure 29: Comparison of measured and simulated EF level trigger efficiency for various XS triggers for W eν events. Because it involves a sum over the full calorimeter, the efficiency behavior may vary → miss significantly for different event samples. The structure near 40 GeV offline ET in some of these plots W arises from the cut on the mT used in selecting these events to reduce QCD background.

28 1 1

Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 L1 XS15 + EF XS30 0.4 L1 XS30 + EF XS45

1 1

Efficiency 0.8 Efficiency 0.8

0.6 0.6

0.4 L1 XS45 + EF XS60 0.4 L1 XS50 + EF XS75

Data 2011 Data 2011 0.2 MC W → e ν 0.2 MC W → e ν ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV ATLAS Preliminary, ∫ L dt = 4.7 fb-1, s = 7 TeV 0 0 0 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 140 160 180 200 220 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T Figure 30: Comparison of measured and simulated combined all-level trigger efficiency for various XS triggers for W eν events. Because it involves a sum over the full calorimeter, the efficiency behavior → miss may vary significantly for different event samples. The structure near 40 GeV offline ET in some of W these plots arises from the cut on the mT used in selecting these events to reduce QCD background.

29 1 1

Efficiency ATLAS Preliminary Efficiency ATLAS Preliminary 0.8 0.8 Data 2011 Data 2011 0.6 MC W → µ ν 0.6 MC W → µ ν

0.4 miss 0.4 miss L1 ET > 10 GeV L1 ET > 20 GeV miss miss EF ET > 20 GeV EF ET > 30 GeV 0.2 0.2 ∫ L dt = 4.3 fb-1, s = 7 TeV ∫ L dt = 4.3 fb-1, s = 7 TeV

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T

1 1

Efficiency ATLAS Preliminary Efficiency ATLAS Preliminary 0.8 0.8 Data 2011 Data 2011 0.6 MC W → µ ν 0.6 MC W → µ ν

0.4 miss 0.4 miss L1 ET > 30 GeV L1 ET > 35 GeV miss miss EF ET > 40 GeV EF ET > 50 GeV 0.2 0.2 ∫ L dt = 4.3 fb-1, s = 7 TeV ∫ L dt = 4.3 fb-1, s = 7 TeV

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T

1 1

Efficiency ATLAS Preliminary Efficiency ATLAS Preliminary 0.8 0.8 Data 2011 Data 2011 0.6 MC W → µ ν 0.6 MC W → µ ν

0.4 miss 0.4 miss L1 ET > 40 GeV L1 ET > 50 GeV miss miss EF ET > 60 GeV EF ET > 70 GeV 0.2 0.2 ∫ L dt = 4.3 fb-1, s = 7 TeV ∫ L dt = 4.3 fb-1, s = 7 TeV

0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 (offline, EM scale) Emiss [GeV] (offline, EM scale) Emiss [GeV] T T Figure 31: Comparison of measured and simulated combined all-level trigger efficiency for various XE triggers for W µν events. The transverse momentum of muons is not included in these determina- miss → tions of ET . Because it involves a sum over the full calorimeter, the efficiency behavior may vary significantly for different event samples.

30 7 Lessons for running at higher luminosity

As discussed above, pileup with µ of about 15 required relatively high thresholds for transverse momen- miss tum triggers of L1 XE50 and EF xe70. XS triggers allowed recording some events with lower ET , but it was clear that further increase in luminosity would force thresholds so high that sensitivity to much of the interesting physics would be lost. Based on these findings, several changes were implemented in order to improve the trigger in 2012. Only one of these is described here, as it was tested during the 2011 data-taking period. As mentioned above, the Level 2 algorithm used only the coarse L1 information in 2011. It was clear that a better L2 algorithm needed to be put in place for 2012. At the EF level, the full calorimeter miss information is read out and used to calculate ET , but this is not feasible at L2 due to bandwidth limitations. Instead, the firmware of the calorimeter front-end electronics board (FEB) was modified to provide just a sum over all (up to and mostly 128) cells in each board. Only cells above a certain noise threshold were used in this sum, mimicking the EF-level algorithm. This reduced energy information was made available to the L2 through software modifications to the data acquisition system. Figure 32 shows the gain in resolution achieved by using this FEB information at Level 2 in a test run at the end miss of 2011. Adopting at Level 2 an algorithm such as this one, which returns values of ET , ΣET and XS closer to those determined at Event Filter Level, results in sharper turn-on curves for all of these triggers and therefore better trigger efficiency for the corresponding signal events.

4000 ATLAS Preliminary σ(EF•L2) = 3.7 GeV 3500 ∫L dt ~ 40.3 pb•1 σ(EF•L1) = 12.8 GeV

Events / GeV 3000 s = 7 TeV 2500

2000

1500

1000

500

0•40 •30 •20 •10 0 10 20 30 40 miss ∆ Ex [GeV]

miss Figure 32: Event-by-event diﬀerence between the L2 algorithm and the EF algorithm calculation of ET for an L2 algorithm using L1 value (red) and for the FEB-based (black) L2 algorithm.

8 Summary and conclusion

In 2011, the ATLAS transverse momentum triggers were used to record proton-proton collision data with µ ranging from about 3 to 30 and as a minimally-biased trigger for heavy ion collisions. The large h i change in pileup during the proton-proton data-taking period required tuning of the noise suppression

31 miss scheme and changes in the prescales of ET and ΣET triggers. The qualitative behavior of these triggers miss as µ increased, with large changes in ET and ΣET triggers, but much smaller changes in XS, were miss as expected from their definition and design. Because of rate limitations, the lowest unprescaled ET thresholds had to be raised by 10 to 20 GeV as µ increased. Low threshold trigger rates varied greatly with beam conditions, whereas higher threshold ones had a more regular dependence on µ. Introduction miss of the XS trigger allowed collecting samples of events with ET too low to be recorded with the high miss threshold ET triggers. The performance and efficiency of the various triggers were mostly consistent with what is expected based on simulations, though various effects led to differences in tails of distribu- miss tions. As a whole, these triggers allowed collection of data with high ET at near 100 % efficiency, and miss miss for events with low ET with limited efficiency. Based on 2011 data, specifically the need to raise ET thresholds and the decrease in XS trigger rates as luminosity went up, it was clear that new strategies would, however, have to be developed for the even higher pileup expected for 2012. These included introduction of a new L2 algorithm which uses front end board calorimeter-cell sums. The algorithm was tested in 2011 and found to provide substantial improvement in resolution compared with the 2011 algorithm using L1 values.

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33 PHYSICAL REVIEW D 93, 052009 (2016) Search for magnetic monopoles and stable particles with high electric charges in 8 TeV pp collisions with the ATLAS detector

G. Aad et al.* (ATLAS Collaboration) (Received 29 September 2015; published 18 March 2016) A search for highly ionizing particles produced in proton-proton collisions at 8 TeV center-of-mass energy is performed by the ATLAS Collaboration at the CERN Large Hadron Collider. The data set used corresponds to an integrated luminosity of 7.0 fb−1. A customized trigger significantly increases the sensitivity, permitting a search for such particles with charges and energies beyond what was previously accessible. No events were found in the signal region, leading to production cross section upper limits in the mass range 200–2500 GeV for magnetic monopoles with magnetic charge in the range 0 5 j j 2 0 . gD < g < . gD, where gD is the Dirac charge, and for stable particles with electric charge in the range 10 < jzj < 60. Model-dependent limits are presented in given pair-production scenarios, and model-independent limits are presented in fiducial regions of particle energy and pseudorapidity.

DOI: 10.1103/PhysRevD.93.052009

I. INTRODUCTION 2 1 α ¼ gD ¼ ð Þ m ℏ 4α ; 2 The multi-TeV energy regime accessible at the CERN c e Large Hadron Collider (LHC) enables the exploration of uncharted territories of particle physics. A new massive which is very large, precluding any perturbative calculation of monopole production processes. In terms of ionization particle would represent a dramatic deviation from the energy loss at high velocity, a monopole with the Dirac predictions of the Standard Model, and such a spectacular charge corresponds to an electrically charged particle with discovery would lead to fundamental insights and critical charge jzj ≈ 68.5. A monopolewould thus manifest itself as a theoretical developments. This paper presents a dedicated HIP, as would any highly charged stable particle. In addition search for a long-lived highly ionizing particle (HIP) to the Dirac argument, topological monopole solutions signature in the ATLAS detector. Such a signature differs arise naturally in unification theories with gauge symmetry from those of the known objects (e.g., electrons, muons, breaking [5,6]. Monopole solutions are also allowed in the and jets) reconstructed in ATLAS and would be missed by electroweak theory itself with a mass at the TeV scale and analyses that rely only on such objects. HIP signatures can an elementary magnetic charge that is twice the Dirac arise at LHC energies as an important feature of physics charge [2,7]. beyond the Standard Model, for example, in theories of Searches for monopoles have been carried out in cosmic- magnetic monopoles and dyons, strange quark matter, ray experiments [8–14], in matter [15–18], and at colliders Q-balls, and stable microscopic black-hole remnants [1,2]. [1,19–27]. The high luminosity and energy of LHC The Dirac argument [3,4] addresses the problem of electric collisions mean that monopoles (and other HIPs) can be charge quantization by postulating the existence of particles probed at higher masses and to greater precision than was possessing magnetic charge. The lightest magnetic monop- previously accessible [28]. In 2010, ATLAS initiated the ole would be stable and carry a magnetic charge that is a search for HIPs at the LHC by considering a particle multiple of the Dirac charge gD, i.e., in Gaussian units, producing a region of high ionization density in the 1 1 gDe ¼ ⇒ gD ¼ ≈ 68 5 ð Þ transition radiation tracker (TRT) and slowing down and ℏ 2 2α . ; 1 c e e stopping in the electromagnetic (EM) calorimeter [29]. Since energy loss by bremsstrahlung and eþe− pair where e is the elementary electric charge and α is the fine e production is negligible for HIPs, the ionization energy structure constant. With the introduction of a magnetic deposit in the EM calorimeter is narrower than that monopole, the duality of Maxwell’s equations implies a associated with electrons and photons, which induce an magnetic coupling EM shower. This stopping signature applies to HIPs with charge jzj ≳ 10, while particles with lower charges have * Full author list given at the end of the article. been probed at ATLAS and CMS using a muon-like signature [30,31]. The stopping signature was used at Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri- ATLAS to set the first constraints on the production of bution of this work must maintain attribution to the author(s) and magnetic monopoles carrying a single Dirac charge ’ j j¼1 0 the published article s title, journal citation, and DOI. ( g . gD)inpp collisions at 7 TeV center-of-mass

2470-0010=2016=93(5)=052009(25) 052009-1 © 2016 CERN, for the ATLAS Collaboration G. AAD et al. PHYSICAL REVIEW D 93, 052009 (2016) energy [25]. This first monopole search at the LHC relied 0.5, 4.3, and 16.5 radiation lengths, respectively. The noise on an electron trigger. A new dedicated ATLAS trigger level in the EM calorimeter is typically 200 MeV or less. designed to improve the sensitivity to the stopping HIP The robustness of the EM calorimeter energy reconstru- signature and access new regions of HIP charge is used in ction has been studied in detail and pulse shape predictions the present search. Further improvements with respect to are consistent with the measured signals [34]. the previous analyses include a larger integrated luminosity, Beyond the EM calorimeter, in the barrel region, the higher center-of-mass energy, extension of the signal ATLAS hadronic calorimeter is made of scintillator tiles acceptance to the detector forward regions (pseudorapidity and steel absorber plates. It comprises a barrel in the [32] up to jηj¼2), interpretation for a magnetic charge jgj pseudorapidity range jηj < 1.0 and an extended barrel in up to twice the Dirac charge as well as for an electric charge the range 0.8 < jηj < 1.7. Liquid-argon hadronic end cap jzj between 20 and 60, and an interpretation for spin-0 HIPs calorimeters cover the range 1.5 < jηj < 3.2. The noise in addition to spin-1=2 for the model-dependent limits. level in the hadronic calorimeter is typically 100 MeV or less. II. ATLAS DETECTOR The ATLAS data were filtered by a three-level trigger system that reduced the rate from 20 MHz to ∼400 Hz. The ATLAS experiment [33] is a multipurpose particle Level 1 (L1) is a hardware-based trigger that, for the physics detector with a forward-backward symmetric 4π purposes herein, identifies regions of interest (ROI) asso- cylindrical geometry and near coverage in solid angle. ciated with energy deposits in the calorimeter. The level-2 In the ATLAS detector, the HIP signature can be readily and event filter triggers are implemented in software, with distinguished using the transition radiation tracker in the detector information corresponding to the ROI accessible inner detector (ID) and the liquid-argon sampling electro- by the level-2 trigger, whereas the full detector information magnetic calorimeter. is accessible by the event filter. Tracking in the inner detector is performed by silicon- The stopping power of a HIP in matter depends on its based detectors and an outer tracker, the TRT, using straw charge, mass, and energy (but not on its spin), as well as tubes with particle identification capabilities based on the material traversed along its path. Details of the ATLAS transition radiation. The TRT is divided into barrel geometry are given in Ref. [33] in terms of number of (covering the pseudorapidity range jηj < 1.0) and end 0 77 jηj 2 0 radiation lengths X0, as a function of depth and pseudor- cap ( . < < . ) components. A track typically apidity. In this search, a HIP candidate must deposit energy comprises 32 straw hits. In the front-end electronics of in the EM calorimeter to be selected by the level-1 trigger. the TRT, discriminators are used to compare the straw-tube In 8 TeV collisions, this limits the range of HIP charges signal against low and high thresholds. HIPs would j j ≤ 2 0 that can be probed in ATLAS to g . gD for magnetic produce a large number of high-threshold (HT) hits along charge and jzj ≤ 60 for electric charge. their trajectories, due to both the high ionization of the HIP and the high density of δ-rays emitted from the material III. SIMULATIONS along the trajectory of the HIP. The amount of ionization in a straw tube needed for a TRT HT hit is roughly equivalent The MADGRAPH5 Monte Carlo (MC) event generator to three times that expected from a minimum ionizing [35] is used to estimate production cross sections and to particle. generate signal events where HIPs are produced in pairs A thin superconducting solenoid magnet surrounding from the initial pp state via quark-antiquark annihilation the tracking section of the ATLAS detector produces a field into a virtual photon. This process is modeled by assuming of approximately 2 T parallel to the beam axis. The ID leading-order Drell-Yan (DY) heavy charged-particle and solenoid together represent an amount of material of pair production, where the coupling is obtained by scaling approximately two radiation lengths for jηj < 0.7 and three the photon-electron coupling by the square of the HIP radiation lengths elsewhere. electric or magnetic charge (e.g., a factor 68.52 for a Dirac Liquid-argon sampling EM calorimeters, which com- monopole). In the absence of a consistent theory describing prise accordion-shaped electrodes and lead absorbers, the coupling of the HIP to the Z boson, such a coupling is surround the ID and solenoid. The EM calorimeter in set to zero in the MADGRAPH5 model. HIP production the pseudorapidity ranges jηj < 1.475 (barrel) and 1.375 < models suffer from large uncertainties due to the large jηj < 2.5 (end cap) is segmented transversely and divided coupling of the HIP to the photon precluding any pertur- into three layers in depth, denoted as the first (EM1), bative calculation beyond leading order. For magnetic second (EM2), and third (EM3) layer, respectively. In the monopole pair production, the coupling is described by pseudorapidity range jηj < 1.8, an additional presampler Eq. (2). The CTEQ6L1 [36] parton distribution functions of layer in front of the accordion calorimeter is used to provide the proton are employed and PYTHIA version 8.175 [37,38] a measurement of the energy lost in front of the calorim- is used for the hadronization and the underlying-event eters [33]. The presampler, EM1, and EM2 layers in the generation. Direct pair production implies that the HIPs are barrel represent an amount of material of approximately not part of a jet and are thus isolated.

052009-2 SEARCH FOR MAGNETIC MONOPOLES AND STABLE … PHYSICAL REVIEW D 93, 052009 (2016) Given the production model uncertainties, the impact confidence in the modeling of the relevant observables. that a change in model would have on the angular These are labeled W → νe and DY → eþe− and corre- distributions and cross sections is investigated by also spond to electroweak processes in which W bosons, and Z considering spin-0 DY HIP production. In addition to lower bosons or virtual photons, decay to electrons. Both samples cross sections, angular momentum conservation dictates are generated with POWHEG [44] and then passed through that DY production of spin-0 HIPs is suppressed near the PYTHIA8 with the AU2 CT10 set of tuned MC parameters phase-space thresholds due to the fact that the intermediate [45] for hadronization and parton showering. (virtual) photon has spin-1. Thus, spin-1=2 and spin-0 HIPs have different angular distributions, providing a measure IV. TRIGGER of how model uncertainties affect the search acceptance. At level 2, standard ATLAS EM triggers implicitly The spin-0 samples are generated using MADGRAPH5, as require energy deposition in the EM2 layer and thus are described above. unable to capture HIPs that stop in EM1 or in the The model-independent interpretation does not assume a presampler. Furthermore, conditions for 8 TeV collisions particular production mechanism. For this, single-particle include either high thresholds on the transverse energy, HIP samples with uniform distributions in HIP kinetic ¼ θ 3000 ET E sin , for photon triggers or tight requirements on energy and pseudorapidity, in the ranges Ekin < GeV jηj 2 5 track quality and isolation for electron triggers (severely and < . , respectively, are used to determine the impairing HIP searches due to the effects of long-range selection efficiencies in regions of kinematic phase space. δ-rays). Thus, a new level-2 trigger dedicated to HIP Since the interaction of HIPs with material is spin inde- searches was developed and deployed in 2012. The pendent [39,40], these efficiencies are identical for spin-0 level-2 HIP trigger has no EM energy requirements beyond 1 2 and spin- = HIPs. level-1 and yields the maximum acceptance to HIPs that the The DY and single-particle samples, which have approx- ATLAS geometry can possibly allow using calorimeter- imately 20 000 and 50 000 events, respectively, are pro- based level-1 triggers. Crucially, this provides access to duced for HIPs with masses m equal to 200, 500, 1000, HIPs with higher charges and lower energies. A low rate 1500, 2000, and 2500 GeV. For each mass point, magnetic is achieved by imposing requirements on the number j j monopoles are simulated for magnetic charges g (in units and fraction of TRT HT hits in a narrow region around of the Dirac charge gD) 0.5, 1.0, 1.5, and 2.0. Separate the level-1 calorimeter ROI. samples of HIPs are produced with electric charges jzj (in units of the elementary charge) 10, 20, 40, and 60. A. HIP trigger selection The single-particle and spin-1=2 DY samples are processed by the ATLAS detector simulation [41] based on The lowest threshold unprescaled level-1 calorimeter trigger [46] in 2012 is used to seed the level-2 HIP trigger. GEANT4 [42]. In addition to the standard ionization process The L1 trigger selects calorimeter towers exceeding an based on the Bethe-Bloch formula, the particle interaction η model includes secondary ionization by δ-rays. For monop- -dependent ET threshold between 18 and 20 GeV and oles, a modified Bethe-Bloch formula is used to account for containing less than 1 GeV in the corresponding region of the velocity-dependent Lorentz force [39,40]. The effect of the hadronic calorimeter. The hadronic energy veto has a the ATLAS solenoid magnetic field (bending of trajectories small impact on a HIP pair-produced signal in 8 TeV collisions, since only a negligible fraction of HIP candi- of electrically charged particles and acceleration of mag- dates with equivalent charge 1.0g or higher would possess netic monopoles) is included in the equations of motion. D enough energy to enter the hadronic calorimeter. A correction for electron-ion recombination effects in the ’ The HIP trigger algorithm reconstructs two variables: the EM calorimeter (Birks law) is applied, with typical visible trig energy fractions between 0.1 and 0.4 for the signal particles number of TRT HT hits, NHT, and the fraction of all TRT trig 0 015 ϕ considered [43]. Trigger efficiency losses for slow particles hits that are HT hits, fHT, in a wedge of . rad in arriving at the calorimeter later than highly relativistic defined within the level-1 ROI. The center of this wedge is particles (and therefore being assigned to the wrong bunch determined as the location of the bin with the highest crossing) are simulated. Particles arising from multiple number of TRT HT hits among 20 bins each of 0.01 rad interactions in the same or neighboring bunch crossings in ϕ around the ROI center. The ROI η information is also (“pileup”) are overlaid on both the pair-production and used to identify and count only the hits in the parts of the single-particle samples to reflect the conditions of the data TRT that cover the corresponding η regions. trig 20 trig 0 37 sample considered in the search. This full detector simu- The selection was defined as NHT > and fHT > . lation of HIPs uses significant computing resources and, as a compromise between controlling the rate and ensuring hence, was not performed for spin-0 DY HIPs. a high signal efficiency. The rate of events passing these A data-driven method is used to estimate backgrounds requirements is dominated by chance occurrences in multi- surviving the final selections (see Sec. VI). Two samples jet events where more HT hits than usual are produced of simulated background events are used to increase in the ϕ wedge defined by the trigger, either due to

052009-3 G. AAD et al. PHYSICAL REVIEW D 93, 052009 (2016) overlapping charged particles within the same straws or due not require energy deposits in EM2, allowing the to electronic noise. reconstruction of clusters from HIPs that stop in EM1 or in the EM presampler in addition to those that stop in EM2. B. Trigger performance in 8 TeV collisions In the TRT barrel, the TRT hit-counting region is a The HIP trigger rate was in the range 0.4–0.7 Hz from rectangular road of constant width 4 mm in the transverse its deployment in September 2012 until December 2012. plane centered around the region in ϕ with the highest The integrated luminosity collected during this period was density of HT hits. In the TRT end cap, a wedge of 7.0 fb−1 of 8 TeV proton-proton collision data. The rate is Δϕ ¼0.006 is used instead. The hit-counting procedure found to be lower at higher instantaneous luminosities, is described in more detail in Ref. [25]. which correspond to the beginning of the runs when more The selection is designed to reduce Standard Model populated bunches produce higher pileup. This is explained backgrounds while retaining HIP signal candidates and trig by the observation that fHT is sensitive to pileup: additional relies on the following variables: collisions per bunch crossing produce additional soft tracks (i) fHT: the fraction of TRT HT hits in a road or wedge, as that contaminate the ϕ wedge with low-threshold hits, described above, matched to an EM cluster. Com- thus reducing the HT hit fraction. This can affect the signal pared to how the TRT hits are counted in Ref. [25],a efficiency as well. slight improvement is made in the central (jηj < 0.1) The dedicated HIP trigger provides a considerable region and in the TRT barrel–end cap transition acceptance gain by capturing HIP candidates that stop in region (0.77 < jηj < 1.06), which yields a higher the first EM calorimeter layer, or even in the EM presam- signal efficiency. In the central region, the TRT is η 0 η 0 pler. With 2012 pileup conditions, a monopole candidate split between < and > barrels and fHT is that is within the acceptance of the TRT and has passed computed separately for each TRT component. The the level-1 trigger requirements would have a high (≳90%) maximum value obtained from either of these com- probability to satisfy the HIP trigger algorithm. The ponents separately or combined is selected as the new efficiency drops off for HIP candidates of sufficiently high fHT value. Similarly, in the transition region, fHT is energy that have a high probability to penetrate through to recomputed by considering the barrel and the end the hadronic calorimeter and provoke the level-1 hadronic cap separately as well as together. veto. The available models of HIP production predict the (ii) E0, E1, and E2: the energy belonging to an EM energy distribution to peak in the range 100–500 GeV (see calorimeter cluster contained in the presampler, Ref. [28] and references therein), in which a large fraction EM1, and EM2, respectively. j j¼1 0 of g . gD monopole candidates are recovered by the (iii) w0, w1, and w2: the fraction of EM cluster energy HIP trigger, as compared to existing photon triggers. As contained in the two most energetic cells in the an example, the HIP trigger acceptance times efficiency presampler, four most energetic cells in EM1, and in the DY spin-1=2 monopole pair-production model five most energetic cells in EM2, respectively. This j j¼1 0 ¼ 1000 ð24 6 0 3Þ% for g . gD and m GeV is . . , provides a measure of the energy dispersions in while for the 120 GeV single-photon trigger it is only each EM calorimeter layer, with values around ð3.1 0.1Þ%. For the charges and masses considered in unity (occasionally exceeding unity due to negative this search, only HIPs with β > 0.4 would be energetic cell-noise energies) corresponding to the minimum enough to reach the EM calorimeter to be selected by the dispersion, as expected for HIPs. The number of L1 trigger. The introduction of the HIP trigger reduces the cells chosen was optimized by maximizing the j j¼2 0 minimum kinetic energy needed to trigger on g . gD discrimination power between HIPs and electron monopoles from ∼1500 GeV to ∼900 GeV. backgrounds, accounting for the different granularities in the different EM calorimeter layers. V. EVENT SELECTION (iv) w: a combination of the three energy dispersion variables above, defined as the arithmetic mean The event selection starts by identifying energy deposits of all wi (i ¼ 0,1,2) for which Ei exceeds a 5 GeV (“clusters”) in the EM calorimeter and associating them threshold. This threshold ensures that the energy with a region with a high fraction of HT hits in the TRT. dispersion in a layer that is not traversed by a EM cluster candidates are constructed by the EM topo- HIP is not included, since this layer would mostly logical cluster algorithm [47], which starts with a seed EM contain noise. calorimeter cell with large signal-to-noise ratio, iteratively The selection criteria, defined below, are chosen so as to adds neighboring cells with a threshold defined as a minimally impact the signal efficiency. The optimal fHT function of the expected noise, and finishes by including and w cut values that define the signal region maximize the all direct neighbor cells on the outer perimeter. This ratio of signal over square root of the background across all algorithm is very efficient for reconstructing clusters from mass and charge points. The background contribution is − HIP energy depositions. Topological cluster formation does obtained from w fHT pseudodata generated by randomly

052009-4 SEARCH FOR MAGNETIC MONOPOLES AND STABLE … PHYSICAL REVIEW D 93, 052009 (2016) sampling the individual one-dimensional distributions of TABLE I. Number of events at each stage of the selection in fHT and w in collision data. In order to exclude the data and in representative simulated signal samples (DY spin- 1 2 ¼ 1000 j j¼1 0 j j¼40 possibility of generating data points from the signal region = , m GeV, and charges g . gD and z ). See in the pseudodata, only candidate events with w<0.8 text for descriptions of the selection criteria. The percentages given in parentheses are relative efficiencies with respect to are used to generate the one-dimensional fHT distribution 0 6 previous lines. and candidate events with fHT < . are used to generate the one-dimensional w distribution. At each stage, events Data jgj¼1.0gD jzj¼40 without any candidates satisfying the criteria are discarded. Total MC 26 502 23 848 (1) The HIP trigger criteria must be satisfied. 16 Level-1 trigger 7962 (30.0%) 6319 (26.5%) (2) Preselection: clusters with ET > GeV in the EM HIP trigger 854 130 6526 (82.0%) 4481 (70.9%) calorimeter and associated with a region in the TRT Preselection 600 358 (70.3%) 6503 (99.7%) 4431 (98.9%) 0 4 satisfying fHT > . are selected. This efficiently EM layers 591 627 (98.5%) 6503 (100%) 4421 (99.8%) identifies the cluster candidates that triggered the Pseudorapidity 501 304 (84.7%) 6242 (96.0%) 4072 (92.1%) event, plus possible additional candidates in the Hadronic veto 498 993 (99.5%) 6242 (100%) 4071 (100%) same event. If multiple candidates are found within EM dispersion 3 6224 (99.7%) 4065 (99.9%) a window Δϕ × Δη ¼ 0.05 × 0.1, only the cluster TRT HT hits 0 6195 (99.5%) 4018 (98.8%) with the highest summed energy in the presampler and EM1 layers is kept. (3) EM layers: it is required that at least one of the of the level-1 trigger hadronic veto is well accounted E0 > 5 GeV or E1 > 5 GeV requirements is satis- for in the simulation. fied for the selected cluster candidate. This rejects (6) Single candidate: in case of multiple candidates backgrounds where there is only energy in EM2 in the same event, only the candidate with highest (while a HIP penetrating EM2 must necessarily have fHT is kept. This has a negligible impact on signal also gone through the preceding layers). efficiencies while ensuring a consistent event-based (4) Pseudorapidity: cluster candidates are selected in background estimate from data. the range 0 < jηj < 1.375 or 1.52 < jηj < 2.0. The (7) EM dispersion: candidates with w ≥ 0.94 are EM calorimeter barrel–end cap transition regions selected. ≥ 0 70 are excluded to ensure the robustness of the w (8) TRT HT hits: candidates with fHT . are variable. selected. (5) Hadronic veto: cluster candidates with less than The last two selection criteria on w and fHT are very 1 GeV hadronic calorimeter energy calculated using effective at reducing backgrounds and at the same time the hadronic barrel and extended barrel calorimeters retaining potential signals, as shown in Table I and in Fig. 1. are selected. This criterion ensures that the efficiency These two variables are only slightly correlated, such

108 ATLAS 108 ATLAS s = 8 TeV, 7.0 fb-1 s = 8 TeV, 7.0 fb-1 7 7 10 Data DY spin-1/2 m=1000 GeV, ⎜g ⎜ =1.0g 10 Data DY spin-1/2 m=1000 GeV, ⎜g ⎜ =1.0g D D 6 ± ± 6 ± ± 10 MC W → νe DY spin-1/2 m=1000 GeV, ⎜z ⎜ =40 10 MC W → νe DY spin-1/2 m=1000 GeV, ⎜z ⎜ =40 MC DY → e+e- MC DY → e+e- 105 105

104 104

103 103 Events/0.02 Events/0.02 102 102

10 10

1 1

10-1 10-1 0 0.2 0.4 0.6 0.8 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 w f HT

FIG. 1. Distributions of the EM energy dispersion w (left) and fraction of TRT HT hits fHT (right) at the last stage of the event selection (prior to the requirements on these two variables). Electroweak background MC samples with electrons in the final state (luminosity- weighted) as well as signal samples of various HIP charges and m ¼ 1000 GeV (luminosity-weighted × 500) are also shown. Multijet processes (not simulated) are responsible for most of the candidates observed in data.

052009-5 G. AAD et al. PHYSICAL REVIEW D 93, 052009 (2016) that control regions for the data-driven background esti- performance of the algorithm and a well-defined efficiency mate can be defined (see Sec. VI and Fig. 4). The EM of a region. For some mass and charge points, such regions dispersion w is independent of the HIP mass and charge due are too narrow to be found with this definition, hence, to the absence of an EM shower. The energy loss of a HIP no model-independent cross section limit is obtained for is proportional to the square of the charge. Thus, HIPs those points. In particular, no fiducial region was found with higher charge produce more TRT HT hits, yielding a for HIPs with electric charge jzj¼10 for any mass point. Figure 3 shows the various identified fiducial regions higher fHT. No significant dependence on the HIP mass is in jηj (top left) as well as the regions in Ekin corresponding expected for fHT. T to the two jηj regions in the barrel (top right and bottom kin jηj A. Selection efficiencies in fiducial kinematic regions left) and the regions in EL corresponding to the region in the end cap (bottom right), for all relevant mass and Following the example of previously published charge points. ATLAS HIP searches [25,29], fiducial regions of the HIP kinematic parameter space are identified in which B. Selection efficiencies in pair-production models the selection efficiency is high and uniform. This permits an interpretation of the results that does not depend on the Fully simulated events are used to determine selection assumed model of HIP production. The fiducial regions efficiencies for a DY fermion (spin-1=2) pair-production can be defined in terms of HIP kinetic energy and process for electric as well as magnetic charges. The pseudorapidity and need to be determined separately selection efficiencies for spin-0 DY HIPs, which were for each value of HIP charge and mass, using the fully not fully simulated, are determined as follows: fine effi- simulated single-particle HIP samples described in ciency maps (finely binned in kinetic energy and pseudor- Sec. III. Since the efficiency within the region is uniform apidity) were obtained from fully simulated single-particle by definition, the search results can then be interpreted samples and folded with the generator-level spin-0 DY in any model of HIP production by counting the number angular distributions. As a cross-check, the same method of events within the region. applied to spin-1=2 DY HIPs was found to give results no The minimum particle kinetic energy to which the search more than 9% discrepant from those obtained using the is sensitive depends on the amount of material that a HIP fully simulated spin-1=2 DY sample. needs to traverse before reaching the EM calorimeter. As discussed in Sec. IV B, the main losses in all cases are The maximum energy depends on the amount of material due to the acceptance of the level-1 trigger. In particular, for before the HIP reaches the hadronic calorimeter (where it high charges, a large fraction of the HIPs produced in DY provokes the hadronic veto of the level-1 trigger). From events lose all their energy and stop before they reach the simple geometric considerations, in the EM barrel, this EM calorimeter. The acceptance for DY-produced monop- −1 j j¼2 0 material is roughly proportional to ðsin θÞ , while in the oles with charge g . gD is very small, of the order EM end cap it varies as ðcos θÞ−1. Therefore, the η of 0.1%. For this charge, the ionization energy loss is such dependence of the minimum and maximum energy values that only monopoles with transverse energy higher than can be canceled out to first order by defining them in terms ∼1200 GeV in the barrel and longitudinal energy higher kin ¼ θ ∼1500 of transverse kinetic energy (ET Ekin sin ) in the EM than GeV in the end cap have a chance to pass the barrel region (jηj < 1.475) and longitudinal kinetic energy level-1 trigger. Such energies lie in the extreme tails of kin ¼ θ jηj 1 475 (EL Ekin cos ) in the EM end cap region ( > . ). the 8 TeV DY pair-production energy distributions. High- As can be seen in Fig. 2 in the case of three represen- charge HIPs thus have low acceptances, which are highly kin jηj tative signals, fiducial regions in the ET versus plane dependent on the tails of the distributions, and hence very appear as rectangles for the EM barrel region. Likewise, model dependent. For this reason, the search is not kin jηj rectangles can be defined in the EL versus plane for the interpreted for DY signals with acceptances lower than j j¼2 0 EM end cap regions. The reduced efficiency in the TRT 1%. This includes all g . gD mass points as well as j j¼1 5 ¼ 200 j j¼60 barrel–end cap transition region (0.77 < jηj < 1.06) visible the g . gD, m GeV point and the z , in Fig. 2 (top left) motivates the consideration of a third m ¼ 2000 GeV, and m ¼ 2500 GeV points. region between jηj¼1.0 and the end of the EM calorimeter Full selection efficiencies are presented in Table II for barrel. spin-1=2 and spin-0 HIPs in the DY production model for The rectangles that define the fiducial regions are all masses and charges considered in the search. The mass kin kin determined by first dividing the ET (EL for the EM dependence comes from differences in energy and angular end caps) versus jηj plane into bins of size 25 GeV × 0.05 distributions, and also from the velocity dependence of and using an algorithm that identifies the largest rectangular the energy loss, as more massive HIPs have lower β on region for which the average selection efficiency across all average, which leads to lower energy loss for monopoles bins inside the region is larger than 90% with a standard (or generally higher energy loss for electrically charged deviation lower than 12.5%. The value of the standard particles). Spin-0 HIPs have a higher acceptance due to the deviation cut was chosen as a compromise between narrower angular distribution [35].

052009-6 SEARCH FOR MAGNETIC MONOPOLES AND STABLE … PHYSICAL REVIEW D 93, 052009 (2016) 4500 1 4500 1 ATLAS Simulation ATLAS Simulation 4000 0.9 4000 0.9 m=1000 GeV, ⎜z⎜=40 m=1000 GeV, ⎜z⎜=40 3500 0.8 3500 0.8 0.7 0.7 3000 3000 0.6 0.6 2500 2500 0.5 0.5 [GeV] 2000 [GeV] 2000 kin kin T 0.4 L 0.4

E 1500 E 1500 0.3 0.3 1000 0.2 1000 0.2 500 0.1 500 0.1 0 0 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 ⎜η⎜ ⎜η⎜

4500 1 4500 1 ATLAS Simulation ATLAS Simulation 4000 0.9 4000 0.9 m=1000 GeV, ⎜g⎜=1.0g m=1000 GeV, ⎜g⎜=1.0g D D 3500 0.8 3500 0.8 0.7 0.7 3000 3000 0.6 0.6 2500 2500 0.5 0.5 [GeV] 2000 [GeV] 2000 T L kin 0.4 kin 0.4

E 1500 E 1500 0.3 0.3 1000 0.2 1000 0.2 500 0.1 500 0.1 0 0 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 ⎜η⎜ ⎜η⎜

4500 1 4500 1 ATLAS Simulation ATLAS Simulation 4000 0.9 4000 0.9 m=1500 GeV, ⎜g⎜=2.0g m=1500 GeV, ⎜g⎜=2.0g D D 3500 0.8 3500 0.8 0.7 0.7 3000 3000 0.6 0.6 2500 2500 0.5 0.5 [GeV] 2000 [GeV] 2000 T L kin 0.4 kin 0.4 E 1500 E 1500 0.3 0.3 1000 0.2 1000 0.2 500 0.1 500 0.1 0 0 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 ⎜η⎜ ⎜η⎜

FIG. 2. Total selection efficiency (i.e., the fraction of MC events surviving all the criteria listed in Table I) as a function of transverse kinetic energy (left) or longitudinal kinetic energy (right) and pseudorapidity, for HIPs with mass 1000 GeV and charge jzj¼40 (top), j j¼1 0 j j¼2 0 mass 1000 GeV and charge g . gD (middle), and mass 1500 GeV and charge g . gD (bottom). These plots are obtained using fully simulated single-particle samples with a uniform kinetic energy distribution between 0 and 3000 GeV. The fiducial regions (as defined in the text) are indicated by rectangular dashed lines.

VI. BACKGROUND ESTIMATE despite their lower cross sections. Those are largely The selection criteria defined in Sec. V efficiently reject dominated by W and Z production (described in Standard Model backgrounds. In particular, the vast Sec. III). Electron showers are narrower than jets, and majority of EM cluster candidates in multijet events feature such processes lead to a reconstructed w distribution that broad energy depositions in all three EM layers and few lies closer to the signal region, as can be seen in Fig. 1. Near associated TRT HT hits. Jet backgrounds could pass the full the signal region, candidates from electrons from W and Z selection in cases of extremely rare events in which the EM decays are comparable in yield to candidates from multijet calorimeter shower shape is misreconstructed such as to events. Hot cells in the EM calorimeter do not constitute appear very narrow in all EM layers and the trajectories of backgrounds as they are never found to be associated with several charged particles overlap in the TRT to cross the TRT HT hits while remaining isolated. same set of straws and produce HT hits. Processes featuring A fully data-driven background estimate is performed isolated electrons with transverse momenta exceeding the in this search. This approach is necessary because it is level-1 trigger threshold can also constitute backgrounds, unrealistic to produce the enormous number of MC events

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|z|=20 |z|=20 |g|=2.0g |g|=2.0g D D |g|=1.5g |g|=1.5g D D |g|=1.0g |g|=1.0g D D |g|=0.5g |g|=0.5g D D 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 500 1000 1500 2000 2500 η kin | | ET [GeV]

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|z|=20 |z|=20 |g|=2.0g |g|=2.0g D D |g|=1.5g |g|=1.5g D D |g|=1.0g |g|=1.0g D D |g|=0.5g |g|=0.5g D D 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 3000 kin kin ET [GeV] EL [GeV]

FIG. 3. Fiducial regions for the HIP charges considered in the search, as defined in Sec. VA. The various line styles correspond to different HIP masses. The top left plot shows the jηj acceptance ranges, while the other plots show the Ekin acceptance ranges corresponding to the three different jηj ranges. Blank space means that no fiducial region of high efficiency is found for the corresponding mass and charge. required to model the QCD background, but it also ensures and TRT HT hit criteria are shown in Fig. 4 in the plane that all possible background sources, including those not defined by the two remaining discriminating variables, fHT foreseen, are taken into account. The candidates passing the and w. This plane is divided into A, B, C, and D regions, selection requirements except for the final EM dispersion where A is the signal region. The main assumption on

TABLE II. Event selection efficiencies (i.e., the fraction of MC events surviving all the criteria listed in Table I) in percent for spin-1=2 (top) and spin-0 (bottom) HIPs with DY production kinematic distributions. The quoted uncertainties are due to MC sample size. j j¼0 5 j j¼1 0 j j¼1 5 j j¼10 j j¼20 j j¼40 j j¼60 m (GeV) g . gD g . gD g . gD z z z z spin-1=2 200 22.3 0.33.5 0.10.14 0.03 3.8 0.19.7 0.211.9 0.23.1 0.1 500 33.5 0.314.9 0.31.16 0.09 6.7 0.219.0 0.320.0 0.36.2 0.2 1000 27.8 0.323.4 0.33.7 0.110.7 0.224.6 0.316.9 0.33.8 0.1 1500 23.7 0.322.2 0.33.5 0.113.8 0.222.5 0.310.0 0.21.43 0.09 2000 16.7 0.316.5 0.32.8 0.115.5 0.317.5 0.33.7 0.10.24 0.03 2500 9.8 0.29.8 0.21.61 0.09 12.3 0.210.2 0.21.05 0.07 0.009 0.007 spin-0 200 42.5 0.310.0 0.20.40 0.04 5.9 0.228.0 0.327.6 0.38.2 0.2 500 53.8 0.334.8 0.34.1 0.19.8 0.235.3 0.342.1 0.315.1 0.2 1000 44.3 0.351.1 0.311.4 0.215.1 0.245.7 0.337.5 0.311.4 0.2 1500 36.5 0.349.7 0.313.8 0.219.9 0.347.7 0.326.7 0.34.8 0.1 2000 30.9 0.341.6 0.310.9 0.225.5 0.343.6 0.313.2 0.21.15 0.07 2500 22.9 0.330.8 0.36.9 0.226.9 0.331.7 0.34.3 0.10.18 0.03

052009-8 SEARCH FOR MAGNETIC MONOPOLES AND STABLE … PHYSICAL REVIEW D 93, 052009 (2016) 1.2 ATLAS DY spin-1/2 800 fraction (more than ∼20%) of the signal for HIPs with -1 |g| = 1.0g j j¼0 5 j j¼10 j j¼20 1.1 s = 8 TeV, 7.0 fb D low charges ( g . gD, z , and z ), which m = 1000 GeV 700 1 produce fewer HT hits in the TRT on average. Before even B A 600 knowing how many data events are observed in the signal 0.9 500 region A, it is possible to estimate the expected limit on

HT 0.8 this number from a background estimate that takes signal

f 400

0.7 Events contamination into account in a likelihood fit. Applying 300 DC this method, it is found that signal contamination does not 0.6 200 affect the expected limits in any significant way. As a cross- 0.5 check, the expected number of background events in C is 100 Data estimated by performing fits to the w distribution observed 0.4 0 0 0.2 0.4 0.6 0.8 1 1.2 in D assuming power-law and exponential functions, which w both describe well the falling part of the distribution. Taking into account uncertainties obtained by using differ- FIG. 4. Candidates seen in data (color scale) and in a repre- ent functions and varying the fit parameters, the extrapo- sentative simulated signal sample (black squares) in the fHT lation predicts 4.7 1.0 events in C, compatible with versus w plane, at the last stage of the event selection (prior to the requirements on these two variables). The number of background the three observed events. The fact that the three events events in the signal region (A) is estimated using the left and in C do not appear at w values near the peak of the signal bottom bands (B, D, and C) as control regions, as described in distributions (at w ∼ 1) further supports the claim that they the text. are not due to low-charge HIPs. The observed event yields in quadrants B, C, and D, which the background estimation method relies is that the are 626, 3, and 4615, respectively. The estimated number ratio of region-A to region-C background events is the same of background events in the signal region A, taking into as the ratio of region-B to region-D background events, or, account statistical uncertainties and systematic uncertainties due to possible correlations, is in other words, that fHT and w are independent variables. Detector geometry effects give rise to a correlation due to BC jηj est ¼ ¼ 0 41 0 24ð Þ0 16ð Þ the slight pseudorapidity ( ) dependence of the fHT and w Abkg . . stat . syst : variables. The correlation is small near the signal region but D increases somewhat at lower w values. This motivates the choice of w ¼ 0.84 as the lower w limit of the B and D VII. SYSTEMATIC UNCERTAINTIES control regions. The lower fHT limit of the C and D control Systematic uncertainties that can affect the estimated trig regions is governed by the fHT requirement applied by the signal efficiencies are summarized below. These mostly level-2 HIP trigger. The absolute value of the Pearson concern possible imperfections in the description of the correlation coefficient is below 0.05 in the control regions. detector response to HIPs by the simulation. Given that the expected background is low, the correlations (i) Electron-ion recombination effects in the sampling near the signal region are small, and the limited number of region of the EM calorimeter result in the loss of part events precludes dividing the signal region into several of the energy deposition at high dE=dx values. The separate jηj regions, the data in the whole jηj range are fraction of visible energy is modeled in the ATLAS used without correction to estimate the backgrounds. The simulation using a modified Birks’ law parameter- maximum possible difference between the ratios A/C and ization fitted to heavy-ion measurements in liquid B/D due to correlations is estimated as follows. The B and argon [43]. Varying the fraction of visible energy D regions are extended to cover the range 0.69 i), the weighted average of the ratios Bj=Dj scription used by the GEANT4 simulation. Varying across all bins j>iis computed. This weighted average the simulated material density in the inner detector deviates from Bi=Di by no more than 40%, which is taken within the assumed uncertainties (which can range as the systematic uncertainty in the background estimate from 5% to 15% [48]) leads to a ∼5% uncer- obtained when assuming no correlations. tainty in signal acceptance. This uncertainty is j j¼1 5 j j¼10 Another concern is the possibility of signal contamina- higher for charges g . gD and z with a tion in the control regions. Contamination in B is negligible value of ∼10%. compared to background yields for all signal samples. (iii) Secondary ionization by δ-rays affects the TRT hit However, contamination in C represents a significant patterns. The kinetic energy threshold below which

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σ σ

1 1 DY Spin- 1/2 DY Spin- 1/2 95% CL Limit LO Prediction 95% CL Limit LO Prediction |z|=10 |z|=10 |g|=0.5g |g|=0.5g D D |z|=20 |z|=20 -1 |g|=1.0g |g|=1.0g -1 |z|=40 |z|=40 10 D D 10 |g|=1.5g |g|=1.5g D D |z|=60 |z|=60

0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 m [GeV] m [GeV]

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10 10 [fb] [fb]

σ σ 1 1 DY Spin-0 DY Spin-0 95% CL Limit LO Prediction 95% CL Limit LO Prediction |z|=10 |z|=10 |g|=0.5g |g|=0.5g |z|=20 |z|=20 -1 D D -1 10 |g|=1.0g |g|=1.0g 10 D D |z|=40 |z|=40 |g|=1.5g |g|=1.5g D D |z|=60 |z|=60

0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 m [GeV] m [GeV]

FIG. 5. Cross section upper limits at 95% confidence level for DY HIP production as a function of HIP mass in various scenarios (dashed lines with markers). The upper plots are for spin-1=2 HIP production, whereas the lower plots are for spin-0 HIPs. No cross section limit is shown for mass/charge points with an acceptance lower than 1%. Overlaid on the plots are the leading-order (LO) cross sections (solid lines).

δ-rays are not propagated explicitly in the ATLAS than 10 ns, which corresponds to β < 0.37, there is a simulation depends on the GEANT4 “range cut” significant chance that the event is triggered in the parameter. Varying this parameter results in a next bunch crossing by the level-1 EM trigger. ∼1% uncertainty in the signal efficiency. However, since HIP candidates selected by the (iv) Pileup affects the efficiency as it adds a non- L1 trigger necessarily have β > 0.4, there are no negligible number of TRT low-threshold hits inside significant losses (and no systematic uncertainties) trig the geometrical region considered for the fHT and due to timing effects. ∼1%–3% fHT variables computed by the HIP trigger and the (vii) An uncertainty in the efficiency of offline event selection, respectively. Uncertainties in accounts for the statistical uncertainty from the pileup modeling and TRT hit occupancy result in MC signal samples. ∼3% uncertainty in the signal efficiency. (viii) For spin-0 DY HIPs, the relative uncertainty in (v) Cross-talk effects between EM calorimeter cells efficiency due to the fact that efficiency maps are affect the wi variables, and this is not fully described used instead of a full simulation is ∼9%. in the simulation. The resulting uncertainty in signal In addition to the uncertainties listed above, the system- efficiency is ∼1%. atic uncertainty due to the luminosity measurement is 2.8%. (vi) For clusters delayed with respect to the expected It is derived following the same methodology as that arrival time of a highly relativistic particle by more detailed in Ref. [49].

052009-10 SEARCH FOR MAGNETIC MONOPOLES AND STABLE … PHYSICAL REVIEW D 93, 052009 (2016) TABLE III. Lower mass limits (in GeV) at 95% confidence level in models of spin-1=2 (top) and spin-0 (bottom) DY HIP pair production. These limits are based upon leading-order models, since the production mechanism is of a highly nonperturbative nature.

Drell-Yan lower mass limits (GeV)

jgj¼0.5gD jgj¼1.0gD jgj¼1.5gD jzj¼10 jzj¼20 jzj¼40 jzj¼60 Spin-1=2 1180 1340 1210 780 1050 1160 1070 Spin-0 890 1050 970 490 780 920 880

VIII. RESULTS and electric charge in the range 20 ≤ jzj ≤ 60 with masses −1 between 200 and 2500 GeV. This result is valid in well- Zero events are observed in the signal region in 7.0 fb defined fiducial regions of high and uniform event selection of 8 TeV proton-proton collision data, consistent with the efficiency. Assuming Drell-Yan pair production of spin-1=2 background estimate. This results in an upper limit on the and spin-0 charged massive particles, upper limits on the number of signal events of 3.0 at 95% confidence level in 0 5 ≤ j j ≤ production cross section were obtained for . gD g the data sample. 1 5 10 ≤ j j ≤ 60 . gD and z and masses up to 2500 GeV. These results improve the upper limits on the production A. Cross section limits cross section for HIPs in mass and charge regions acces- Cross section limits are driven by the selection efficien- sible to preceding experiments, and extend the limits to cies (and their uncertainties) for the various signal hypoth- masses higher than 1500 GeV. Monopoles with a magnetic j j¼1 0 j j¼2 0 eses. They are determined using the full CLs frequentist charge higher than g . gD (up to g . gD) and method [50] for each of the HIP masses and charges. In the exotic stable particles with an electric charge higher than fiducial regions, a 90% signal efficiency is used (this comes jzj¼17 (up to jzj¼60) were probed for the first time at from the fiducial region definition, see Sec. VA and Fig. 3). the LHC. The 95% confidence-level cross section upper limit for the fiducial regions is 0.5 fb. The cross section limits for DY ACKNOWLEDGMENTS pair production are shown graphically as functions of mass in Fig. 5. We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions B. Model-dependent mass limits without whom ATLAS could not be operated efficiently. We thank R. Koniuk for useful contributions. We acknowl- As has often been pointed out in the literature (e.g., in edge the support of ANPCyT, Argentina; YerPhI, Armenia; Refs. [1,28]), the accuracy of HIP mass limits is ques- ARC, Australia; BMWFW and FWF, Austria; ANAS, tionable due to the nonperturbative nature of the underlying Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; process, which renders cross section predictions unreliable. NSERC, NRC and CFI, Canada; CERN; CONICYT, However, such limits are still useful for comparing results Chile; CAS, MOST and NSFC, China; COLCIENCIAS, from different searches that make similar theoretical Colombia; MSMT CR, MPO CR and VSC CR, Czech assumptions. In Table III, mass lower limits at 95% con- Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, fidence level are shown, obtained assuming DY production CEA-DSM/IRFU, France; GNSF, Georgia; BMBF, HGF, kinematic distributions for spin-1=2 and spin-0 HIPs. and MPG, Germany; GSRT, Greece; RGC, Hong Kong SAR, China; ISF, I-CORE and Benoziyo Center, Israel; IX. CONCLUSION INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; A search for magnetic monopoles and exotic stable FOM and NWO, Netherlands; RCN, Norway; MNiSW and particles with high electric charge was performed with NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of the ATLAS detector at the LHC using 7.0 fb−1 of 8 TeV pp Russia and NRC KI, Russian Federation; JINR; MESTD, collision data using a signature of a highly ionizing particle Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/ stopping in the EM calorimeter. Candidates were selected NRF, South Africa; MINECO, Spain; SRC and Wallenberg by exploiting the measured ionization in the TRT detector Foundation, Sweden; SERI, SNSF and Cantons of Bern and the shape of the energy deposition in the EM and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; calorimeter. No events were observed in data in the signal STFC, United Kingdom; DOE and NSF, United States region. Upper limits on the production cross section were of America. In addition, individual groups and members set for mass and charge points to which the search proves have received support from BCKDF, the Canada Council, sensitive. A model-independent upper limit on the produc- CANARIE, CRC, Compute Canada, FQRNT, and the tion cross section of 0.5 fb was obtained for signal particles Ontario Innovation Trust, Canada; EPLANET, ERC, 0 5 ≤ j j ≤ 2 0 ł with magnetic charge in the range . gD g . gD FP7, Horizon 2020 and Marie Sk odowska-Curie

052009-11 G. AAD et al. PHYSICAL REVIEW D 93, 052009 (2016) Actions, European Union; Investissements d’Avenir Labex from all WLCG partners is acknowledged gratefully, in and Idex, ANR, Région Auvergne and Fondation Partager particular from CERN and the ATLAS Tier-1 facilities at le Savoir, France; DFG and AvH Foundation, Germany; TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), Herakleitos, Thales and Aristeia programmes co-financed CC-IN2P3 (France), KIT/GridKA (Germany), INFN- by EU-ESF and the Greek NSRF; BSF, GIF and Minerva, CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC Israel; BRF, Norway; the Royal Society and Leverhulme (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 Trust, United Kingdom. The crucial computing support facilities worldwide.

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052009-20 SEARCH FOR MAGNETIC MONOPOLES AND STABLE … PHYSICAL REVIEW D 93, 052009 (2016) (ATLAS Collaboration)

1Department of Physics, University of Adelaide, Adelaide, Australia 2Physics Department, SUNY Albany, Albany, New York, USA 3Department of Physics, University of Alberta, Edmonton, AB, Canada 4aDepartment of Physics, Ankara University, Ankara, Turkey 4bIstanbul Aydin University, Istanbul, Turkey 4cDivision of Physics, TOBB University of Economics and Technology, Ankara, Turkey 5LAPP, CNRS/IN2P3 and Université Savoie Mont Blanc, Annecy-le-Vieux, France 6High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois, USA 7Department of Physics, University of Arizona, Tucson, Arizona, USA 8Department of Physics, The University of Texas at Arlington, Arlington, Texas, USA 9Physics Department, University of Athens, Athens, Greece 10Physics Department, National Technical University of Athens, Zografou, Greece 11Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan 12Institut de Física d’Altes Energies and Departament de Física de la Universitat Autònoma de Barcelona, Barcelona, Spain 13Institute of Physics, University of Belgrade, Belgrade, Serbia 14Department for Physics and Technology, University of Bergen, Bergen, Norway 15Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley, California, USA 16Department of Physics, Humboldt University, Berlin, Germany 17Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 18School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 19aDepartment of Physics, Bogazici University, Istanbul, Turkey 19bDepartment of Physics Engineering, Gaziantep University, Gaziantep, Turkey 19cDepartment of Physics, Dogus University, Istanbul, Turkey 20aINFN Sezione di Bologna, Italy 20bDipartimento di Fisica e Astronomia, Università di Bologna, Bologna, Italy 21Physikalisches Institut, University of Bonn, Bonn, Germany 22Department of Physics, Boston University, Boston, Massachusetts, USA 23Department of Physics, Brandeis University, Waltham, Massachusetts, USA 24aUniversidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil 24bElectrical Circuits Department, Federal University of Juiz de Fora (UFJF), Juiz de Fora, Brazil 24cFederal University of Sao Joao del Rei (UFSJ), Sao Joao del Rei, Brazil 24dInstituto de Fisica, Universidade de Sao Paulo, Sao Paulo, Brazil 25Physics Department, Brookhaven National Laboratory, Upton, New York, USA 26aNational Institute of Physics and Nuclear Engineering, Bucharest, Romania 26bNational Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj Napoca, Romania 26cUniversity Politehnica Bucharest, Bucharest, Romania 26dWest University in Timisoara, Timisoara, Romania 27Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina 28Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 29Department of Physics, Carleton University, Ottawa, ON, Canada 30CERN, Geneva, Switzerland 31Enrico Fermi Institute, University of Chicago, Chicago, Illinois, USA 32aDepartamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile 32bDepartamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile 33aInstitute of High Energy Physics, Chinese Academy of Sciences, Beijing, China 33bDepartment of Modern Physics, University of Science and Technology of China, Anhui, China 33cDepartment of Physics, Nanjing University, Jiangsu, China 33dSchool of Physics, Shandong University, Shandong, China 33eDepartment of Physics and Astronomy, Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai, China 33fPhysics Department, Tsinghua University, Beijing 100084, China 34Laboratoire de Physique Corpusculaire, Clermont Université and Université Blaise Pascal and CNRS/IN2P3, Clermont-Ferrand, France 35Nevis Laboratory, Columbia University, Irvington, New York, USA

052009-21 G. AAD et al. PHYSICAL REVIEW D 93, 052009 (2016) 36Niels Bohr Institute, University of Copenhagen, Kobenhavn, Denmark 37aINFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Italy 37bDipartimento di Fisica, Università della Calabria, Rende, Italy 38aAGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow, Poland 38bMarian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland 39Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland 40Physics Department, Southern Methodist University, Dallas, Texas, USA 41Physics Department, University of Texas at Dallas, Richardson, Texas, USA 42DESY, Hamburg and Zeuthen, Germany 43Institut für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund, Germany 44Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany 45Department of Physics, Duke University, Durham, North Carolina, USA 46SUPA—School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 47INFN Laboratori Nazionali di Frascati, Frascati, Italy 48Fakultät für Mathematik und Physik, Albert-Ludwigs-Universität, Freiburg, Germany 49Section de Physique, Université de Genève, Geneva, Switzerland 50aINFN Sezione di Genova, Italy 50bDipartimento di Fisica, Università di Genova, Genova, Italy 51aE. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia 51bHigh Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 52II Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 53SUPA—School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 54II Physikalisches Institut, Georg-August-Universität, Göttingen, Germany 55Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble, France 56Department of Physics, Hampton University, Hampton, Virginia, USA 57Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, Massachusetts, USA 58aKirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 58bPhysikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 58cZITI Institut für technische Informatik, Ruprecht-Karls-Universität Heidelberg, Mannheim, Germany 59Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan 60aDepartment of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China 60bDepartment of Physics, The University of Hong Kong, Hong Kong, China 60cDepartment of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 61Department of Physics, Indiana University, Bloomington, Indiana, USA 62Institut für Astro- und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria 63University of Iowa, Iowa City, Iowa, USA 64Department of Physics and Astronomy, Iowa State University, Ames, Iowa, USA 65Joint Institute for Nuclear Research, JINR Dubna, Dubna, Russia 66KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 67Graduate School of Science, Kobe University, Kobe, Japan 68Faculty of Science, Kyoto University, Kyoto, Japan 69Kyoto University of Education, Kyoto, Japan 70Department of Physics, Kyushu University, Fukuoka, Japan 71Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 72Physics Department, Lancaster University, Lancaster, United Kingdom 73aINFN Sezione di Lecce, Italy 73bDipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy 74Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 75Department of Physics, Jožef Stefan Institute and University of Ljubljana, Ljubljana, Slovenia 76School of Physics and Astronomy, Queen Mary University of London, London, United Kingdom 77Department of Physics, Royal Holloway University of London, Surrey, United Kingdom 78Department of Physics and Astronomy, University College London, London, United Kingdom 79Louisiana Tech University, Ruston, Louisiana, USA 80Laboratoire de Physique Nucléaire et de Hautes Energies, UPMC and Université Paris-Diderot and CNRS/IN2P3, Paris, France 81Fysiska institutionen, Lunds universitet, Lund, Sweden 82Departamento de Fisica Teorica C-15, Universidad Autonoma de Madrid, Madrid, Spain

052009-22 SEARCH FOR MAGNETIC MONOPOLES AND STABLE … PHYSICAL REVIEW D 93, 052009 (2016) 83Institut für Physik, Universität Mainz, Mainz, Germany 84School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 85CPPM, Aix-Marseille Université and CNRS/IN2P3, Marseille, France 86Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA 87Department of Physics, McGill University, Montreal, QC, Canada 88School of Physics, University of Melbourne, Victoria, Australia 89Department of Physics, The University of Michigan, Ann Arbor, Michigan, USA 90Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, USA 91aINFN Sezione di Milano, Italy 91bDipartimento di Fisica, Università di Milano, Milano, Italy 92B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Republic of Belarus 93National Scientific and Educational Centre for Particle and High Energy Physics, Minsk, Republic of Belarus 94Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA 95Group of Particle Physics, University of Montreal, Montreal, QC, Canada 96P.N. Lebedev Institute of Physics, Academy of Sciences, Moscow, Russia 97Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia 98National Research Nuclear University MEPhI, Moscow, Russia 99D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 100Fakultät für Physik, Ludwig-Maximilians-Universität München, München, Germany 101Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München, Germany 102Nagasaki Institute of Applied Science, Nagasaki, Japan 103Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 104aINFN Sezione di Napoli, Italy 104bDipartimento di Fisica, Università di Napoli, Napoli, Italy 105Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, USA 106Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands 107Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, Netherlands 108Department of Physics, Northern Illinois University, DeKalb, Illinois, USA 109Budker Institute of Nuclear Physics, SB RAS, Novosibirsk, Russia 110Department of Physics, New York University, New York, New York, USA 111Ohio State University, Columbus, Ohio, USA 112Faculty of Science, Okayama University, Okayama, Japan 113Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma, USA 114Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA 115Palacký University, RCPTM, Olomouc, Czech Republic 116Center for High Energy Physics, University of Oregon, Eugene, Oregon, USA 117LAL, Université Paris-Sud and CNRS/IN2P3, Orsay, France 118Graduate School of Science, Osaka University, Osaka, Japan 119Department of Physics, University of Oslo, Oslo, Norway 120Department of Physics, Oxford University, Oxford, United Kingdom 121aINFN Sezione di Pavia, Italy 121bDipartimento di Fisica, Università di Pavia, Pavia, Italy 122Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania, USA 123National Research Centre “Kurchatov Institute” B.P.Konstantinov Petersburg Nuclear Physics Institute, St. Petersburg, Russia 124aINFN Sezione di Pisa, Italy 124bDipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy 125Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania, USA 126aLaboratório de Instrumentação e Física Experimental de Partículas—LIP, Lisboa, Portugal 126bFaculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal 126cDepartment of Physics, University of Coimbra, Coimbra, Portugal 126dCentro de Física Nuclear da Universidade de Lisboa, Lisboa, Portugal 126eDepartamento de Fisica, Universidade do Minho, Braga, Portugal 126fDepartamento de Fisica Teorica y del Cosmos and CAFPE, Universidad de Granada, Granada (Spain), Portugal 126gDep Fisica and CEFITEC of Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal

052009-23 G. AAD et al. PHYSICAL REVIEW D 93, 052009 (2016) 127Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic 128Czech Technical University in Prague, Praha, Czech Republic 129Faculty of Mathematics and Physics, Charles University in Prague, Praha, Czech Republic 130State Research Center Institute for High Energy Physics, Protvino, Russia 131Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom 132aINFN Sezione di Roma, Italy 132bDipartimento di Fisica, Sapienza Università di Roma, Roma, Italy 133aINFN Sezione di Roma Tor Vergata, Italy 133bDipartimento di Fisica, Università di Roma Tor Vergata, Roma, Italy 134aINFN Sezione di Roma Tre, Italy 134bDipartimento di Matematica e Fisica, Università Roma Tre, Roma, Italy 135aFaculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies—Université Hassan II, Casablanca, Morocco 135bCentre National de l’Energie des Sciences Techniques Nucleaires, Rabat, Morocco 135cFaculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Morocco 135dFaculté des Sciences, Université Mohamed Premier and LPTPM, Oujda, Morocco 135eFaculté des sciences, Université Mohammed V, Rabat, Morocco 136DSM/IRFU (Institut de Recherches sur les Lois Fondamentales de l’Univers), CEA Saclay (Commissariat à l’Energie Atomique et aux Energies Alternatives), Gif-sur-Yvette, France 137Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, California, USA 138Department of Physics, University of Washington, Seattle, Washington, USA 139Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom 140Department of Physics, Shinshu University, Nagano, Japan 141Fachbereich Physik, Universität Siegen, Siegen, Germany 142Department of Physics, Simon Fraser University, Burnaby, BC, Canada 143SLAC National Accelerator Laboratory, Stanford, California, USA 144aFaculty of Mathematics, Physics & Informatics, Comenius University, Bratislava, Slovak Republic 144bDepartment of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 145aDepartment of Physics, University of Cape Town, Cape Town, South Africa 145bDepartment of Physics, University of Johannesburg, Johannesburg, South Africa 145cSchool of Physics, University of the Witwatersrand, Johannesburg, South Africa 146aDepartment of Physics, Stockholm University, Sweden 146bThe Oskar Klein Centre, Stockholm, Sweden 147Physics Department, Royal Institute of Technology, Stockholm, Sweden 148Departments of Physics & Astronomy and Chemistry, Stony Brook University, Stony Brook, New York, USA 149Department of Physics and Astronomy, University of Sussex, Brighton, United Kingdom 150School of Physics, University of Sydney, Sydney, Australia 151Institute of Physics, Academia Sinica, Taipei, Taiwan 152Department of Physics, Technion: Israel Institute of Technology, Haifa, Israel 153Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 154Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 155International Center for Elementary Particle Physics and Department of Physics, The University of Tokyo, Tokyo, Japan 156Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan 157Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 158Department of Physics, University of Toronto, Toronto, ON, Canada 159aTRIUMF, Vancouver, BC, Canada 159bDepartment of Physics and Astronomy, York University, Toronto, ON, Canada 160Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 161Department of Physics and Astronomy, Tufts University, Medford, Massachusetts, USA 162Centro de Investigaciones, Universidad Antonio Narino, Bogota, Colombia 163Department of Physics and Astronomy, University of California Irvine, Irvine, California, USA 164aINFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy 164bICTP, Trieste, Italy 164cDipartimento di Chimica, Fisica e Ambiente, Università di Udine, Udine, Italy 165Department of Physics, University of Illinois, Urbana, Illinois, USA 166Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden

052009-24 SEARCH FOR MAGNETIC MONOPOLES AND STABLE … PHYSICAL REVIEW D 93, 052009 (2016) 167Instituto de Física Corpuscular (IFIC) and Departamento de Física Atómica, Molecular y Nuclear and Departamento de Ingeniería Electrónica and Instituto de Microelectrónica de Barcelona (IMB-CNM), University of Valencia and CSIC, Valencia, Spain 168Department of Physics, University of British Columbia, Vancouver, BC, Canada 169Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada 170Department of Physics, University of Warwick, Coventry, United Kingdom 171Waseda University, Tokyo, Japan 172Department of Particle Physics, The Weizmann Institute of Science, Rehovot, Israel 173Department of Physics, University of Wisconsin, Madison, Wisconsin, USA 174Fakultät für Physik und Astronomie, Julius-Maximilians-Universität, Würzburg, Germany 175Fachbereich C Physik, Bergische Universität Wuppertal, Wuppertal, Germany 176Department of Physics, Yale University, New Haven, Connecticut, USA 177Yerevan Physics Institute, Yerevan, Armenia 178Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules (IN2P3), Villeurbanne, France

† Deceased. aAlso at Department of Physics, King’s College London, London, United Kingdom. bAlso at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan. cAlso at Novosibirsk State University, Novosibirsk, Russia. dAlso at TRIUMF, Vancouver BC, Canada. eAlso at Department of Physics, California State University, Fresno CA, United States of America. fAlso at Department of Physics, University of Fribourg, Fribourg, Switzerland. gAlso at Departamento de Fisica e Astronomia, Faculdade de Ciencias, Universidade do Porto, Portugal. hAlso at Tomsk State University, Tomsk, Russia. iAlso at CPPM, Aix-Marseille Université and CNRS/IN2P3, Marseille, France. jAlso at Universita di Napoli Parthenope, Napoli, Italy. kAlso at Institute of Particle Physics (IPP), Canada. lAlso at Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom. mAlso at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia. nAlso at Louisiana Tech University, Ruston LA, United States of America. oAlso at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain. pAlso at Graduate School of Science, Osaka University, Osaka, Japan. qAlso at Department of Physics, National Tsing Hua University, Taiwan. rAlso at Department of Physics, The University of Texas at Austin, Austin TX, United States of America. sAlso at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia. tAlso at CERN, Geneva, Switzerland. uAlso at Georgian Technical University (GTU),Tbilisi, Georgia. vAlso at Manhattan College, New York NY, United States of America. wAlso at Hellenic Open University, Patras, Greece. xAlso at Institute of Physics, Academia Sinica, Taipei, Taiwan. yAlso at LAL, Université Paris-Sud and CNRS/IN2P3, Orsay, France. zAlso at Academia Sinica Grid Computing, Institute of Physics, Academia Sinica, Taipei, Taiwan. aaAlso at School of Physics, Shandong University, Shandong, China. bbAlso at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia. ccAlso at Section de Physique, Université de Genève, Geneva, Switzerland. ddAlso at International School for Advanced Studies (SISSA), Trieste, Italy. eeAlso at Department of Physics and Astronomy, University of South Carolina, Columbia SC, United States of America. ffAlso at School of Physics and Engineering, Sun Yat-sen University, Guangzhou, China. ggAlso at Faculty of Physics, M.V.Lomonosov Moscow State University, Moscow, Russia. hhAlso at National Research Nuclear University MEPhI, Moscow, Russia. iiAlso at Department of Physics, Stanford University, Stanford CA, United States of America. jjAlso at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary. kkAlso at University of Malaya, Department of Physics, Kuala Lumpur, Malaysia.

052009-25 arXiv:1301.6530v2 [hep-ex] 3 Apr 2013 li lcrccag uniain[,2.The the charge that magnetic fundamental predicts 2]. ex- argument [1, to quantisation quantisation means Dirac a charge as electric Dirac plain by 1931 in postulated definition esqatt)i utpeo h ia charge: Dirac the of multiple g a is quantity) less ihteLreHdo oldr[1 2.How- 12]. [11, Collider Hadron Large HERA investigated the being LEP, with are and high-energy the [5–10] Tevatron past including and at colliders explored particle been have tion time. later a the at reaching and System monopoles Solar System, free Solar denotes the “cosmic” of formation stardust the in before trapped already “stellar” monopoles paper, a denotes this form Throughout to space halo. open galactic through freely bod- move astronomical or inside ies conservation, reside charge either iso- they sta- magnetic and are of If they virtue by Nature, work- search. ble in a present exist as monopoles the assumed lated in is hypothesis binding hard ing Such order a assuming the [4]. when core of keV hundred energies several of binding with to coupling, moment magnetic bind through would nuclei monopoles non-zero-spin that indicate theory monopole. a the of on mass constraints theoretical tight no generally ol yial aemse fteodro the ( of order scale the unification of masses monopoles have unification typically theo- would grand Although unification [3]. grand funda- ries in also ingredients are mental monopoles Magnetic number. h xsec fmgei oooe was monopoles magnetic of existence The intrso ietmnpl arproduc- pair monopole direct of Signatures quantum nonrelativistic within Calculations = 7 rmteAci n naci ra,wsaaye.N monopo w 9 No among of analysed. sites, limit was selected areas, upper various Antarctic level from throu and rocks Arctic samples the of rock from kg igneous 24.6 t of of using t passage total conducted in was the enhanced monopoles following be magnetic current to for search expected A be would poles. Earth the inside trapped odcVlaooia etr nttt fErhSciences Earth of Institute Center, Volcanological Nordic o ra ag fvle fmgei oooems n char and mass monopole magnetic of values of range broad a For Ng 2 eateto at cecs ws eea nttt fTe of Institute Federal Swiss Sciences, Earth of Department D q m with erhfrmgei oooe nplrvlai rocks volcanic polar in monopoles magnetic for Search .Bendtz, K. si Iuisand units SI in is 5 eateto hsc,LnatrUiest,Lnatr U Lancaster, University, Lancaster Physics, of Department g .Michael, P. 6 D m eateto esine ahsUiest,Aru,Denm Aarhus, University, Aarhus Geoscience, of Department 4 eateto esine,Uiest fTla us,USA Tulsa, Tulsa, of University Geosciences, of Department 68 = ∼ . 3 8 1 ´ preetd hsqeNcár tCorpusculaire, Nucléaire et Physique Département de 1 · 10 yiu,SokomUiest,Sokom Sweden Stockholm, University, Stockholm Fysikum, 10 .Milstead, D. . and 5 16 − nvriyo eea eea Switzerland Geneva, Geneva, of University 4 5 q ga ssto h oooedniyi h erhsamples. search the in density monopole the on set is /gram e) hr are there GeV), g m .Sloan, T. sadimension- a is = N gec ninteger an 1 i this (in .P Hächler,H.-P. 5 .Tegner, C. eemle uigterfrainadthis differentiation. and chemical large-scale formation to their lead has during molten were ig- latitudes. terrestrial high in at presents rocks monopoles work neous for This search 37], first [36, 35]. the surface [30, meteorites Moon’s [30– in the crust and from Earth’s rocks the in from 35], samples of kilo- of grams hundreds in sought monopoles been Trapped previously have list). complete a here; for given [29] flux are see results [15–28] the significant Earth most on the on (only detec- constraints incident monopoles array tight cosmic set with of These sought been tors. have flight Monopoles experiments. in fluxes by and constrained abundances be can rays, be have cosmic or would in bodies present monopoles astronomical relic inside accumulated extent describe which that to models adequate no presently there during are though matter Even to nucleosynthesis. bound primordial which have by may mechanisms monopoles detailed the are and unknowns cross section annihilation Other monopole-antimonopole the [14]. abun- predictions monopole different dance very make vari- pro- can been the posed have which However, scenarios inflationary ous [13]. noncatas- abundances allow to down trophic inflation diluted be Uni- cosmological to early monopoles of relic very out Models the produced in verse. relics equilibrium as thermal that of assumed exist is may and it scale monopoles scale, weak unification the grand between monopoles the range probes mass pro- which the work, collider in this current In within grams. produced can- TeV be 7 above not masses with monopoles ever, 6 ag lntr oissc steEarth the as such bodies planetary Large 2 n .B Thorarinsson B. S. and nvriyo cln,Reykjav`ık, Iceland Iceland, of University , .M Hirt, M. A. haSUDbsdmgeoee.A magnetometer. SQUID-based a gh ih2. gaemnl-eie rocks mantle-derived are kg 23.4 hich esgaueo nidcdpersistent induced an of signature he e eefudada9%confidence 90% a and found were les emnl eet h geomagnetic the beneath mantle he hooy uih Switzerland Zurich, chnology, e h bnac fmonopoles of abundance the ge, 2 .Mermod, P. ie Kingdom nited ark 7 3, ∗ 2

During this early phase stellar monopoles, if to the magnetic charge. Over geologic time present, will likely have sunk to the planet’s monopoles would migrate towards the magnetic 2 core [38]. Stellar monopoles should therefore axis. At the Earth’s pole, a = 9.8 m s− and 5 · be depleted in planetary crusts, while the deep B = 6.5 10− T, in which case Equation 1 · 13 interiors of planets and stars, as well as the in- yields Asurface =1.2 10 GeV (presently GeV sides of some meteoroids, asteroids and comets, is a unit of mass). A· monopole carrying a sin- 13 would be the only places likely to contain them gle Dirac charge (g = gD) and a mass of 10 in non-negligible amounts. GeV or lower would therefore be expected to Monopoles inside astronomical bodies of be found beneath the Earth’s polar crust and low viscosity possessing stable dipole magnetic in melts below polar regions. A monopole car- fields would move to positions along the mag- rying a multiple of the Dirac charge is allowed netic axis where the magnetic force Fm = qmB to possess a proportionally higher mass. This (B is the vertical component of the magnetic mass bound is conservative because monopoles field) and gravitational force Fg = ma (a is the with equilibrium anywhere inside the mantle gravitational acceleration) are in equilibrium: may still reach the surface through mantle convection (the core-mantle boundary corresponds to A =4 1014 GeV). In a naive model, g ecB g g boundary m = D = A (1) one may assume· that monopoles would be dis- a g g D D tributed randomly throughout the whole man- Although the early configuration of the tle depth up to a distance from the magnetic Earth’s internal magnetic field is poorly known, axis equal to the core radius of 3400 km (this paleomagnetic data suggest that the Earth pos- corresponds to latitudes > 57◦), and absent ev- sessed a dipole field since at least 3.5 billion erywhere else. This results in a concentration years [39–41]. The configuration∼ of the field of monopoles 6 times higher in polar mantle- close to the Earth’s core may be more com- derived rocks than averaged over the Earth’s plex, but the simple assumption of a dipole mass. field over geologic time is reasonable. Carri- The samples used in this search were re- gan estimated that monopoles with g = gD stricted to mantle-derived igneous rocks with and m = 1016 GeV would accumulate near the negligible levels of crustal contamination, em- Earth’s inner core, and developed a model of placed at high (> 63◦) latitudes. Basaltic rocks how monopole annihilation during geomagnetic from hotspots – volcanic regions under which reversals would contribute to the planet’s in- the mantle is thought to be locally hotter, caus- ternal heat, thus limiting the grand-unification- ing an ascending mantle plume – are partic- mass monopole density inside the Earth to less ularly attractive as they are likely to include 4 than 10− /gram [42]. On the other hand, a material from deep inside the mantle. Iceland lighter∼ mass or higher magnetic charge will raise and Hawaii are among the best known exam- the equilibrium depth. We consider monopoles ples of hotspots for which there is evidence attached to nuclei with an equilibrium position that the erupted material comes from more above the core-mantle boundary. Down to a than 600 km depth and possibly as deep as the depth of 2900 km, the Earth’s mantle plays core-mantle boundary [44, 45]. Other active the role of an insulator between the molten hotspot sites at high latitudes, but for which outer core and the crust and has the proper- the role of mantle plumes is debated [46], in- ties of a plastic solid. Although mantle dynam- clude Jan Mayen Island (Arctic Ocean) [47] and ics are complex and various competing geody- Ross Island (Southern Victoria Land, Antarc- namical models exist, it can generally be as- tica) [48]. Large igneous provinces (LIPs) are sumed that the mantle slowly convects as a also of interest for this work. These massive whole, with a full cycle taking approximately magmatic provinces are dominated by exten- 400 500 million years [43]. Monopoles caught sive flood basalt lavas with areal extents of in the− solid mantle would be unable to move > 100000 km2 and igneous volumes of > 100000 freely. Instead, monopoles of both polarities km3, most of which (> 75%) was expelled dur- would be transported up and down along with ing relatively short periods ( 1 5 million mantle convection regardless of the field direc- years) [49]. Furthermore, many∼ LIPs− have been tion. Upon reaching the core-mantle bound- associated with mantle plume activity and con- ary, they would sink through the liquid core tinental break-up [50]. The Kap Washington due to the high mass, before being attracted in Group volcanic sequence (North Greenland) the general direction of the polar regions due and the Skaergaard intrusion (East Greenland) 3

TABLE I. Characteristics of the rock samples used in this search. If not otherwise speciﬁed, they were emplaced during the Cenozoic era. Control samples are indicated with (c). The latitude corresponds to the location at the time of emplacement.

site latitude tectonic setting rock type samples mass (kg) Iceland [56] 64◦ N hotspot, mid-ocean ridge basalt 144 5.916 gabbro 26 1.404 Jan Mayen Island [47] 71◦ N hotspot alkali basalt 6 0.139 Hawaii (c) 21◦ N hotspot tholeiitic basalt 17 0.610 North Greenland [57] 72◦ N LIP, 71-61 million alkali basalt, trachyte, years old trachyandesite, rhyolite 73 1.779 East Greenland [58] 68◦ N LIP, intrusion gabbro 39 1.830 Gakkel Ridge 84◦ N mid-ocean ridge tholeiitic basalt 26 0.707 Mid-Atlantic Ridge (c) 33◦ S mid-ocean ridge tholeiitic basalt 8 0.207 East Pacific Rise (c) 28◦ S mid-ocean ridge tholeiitic basalt 7 0.241 South. Victoria Land 77◦ S hotspot basalt, basanite 233 8.163 North. Victoria Land 72◦ S intraplate volcanism basalt, trachyte 12 0.335 Marie Byrd Land [55] 76◦ S intraplate volcanism alkali basalt (HIMU) 50 2.184 lherzolite 3 0.148 basalt, trachyte 17 0.440 Ellsworth Land 74◦ S intraplate volcanism basalt 11 0.300 Horlick Mountains 87◦ S intraplate volcanism basalt 1 0.021 Antarctic Peninsula (c) 63◦ S subduction zone basalt 5 0.146 Total search 641 23.366 Total control (c) 37 1.204 were considered for this search as parts of the which have been carried up from the mantle High Arctic and North Atlantic LIPs, respec- source rocks without melting. Control samples, tively [51, 52]. Mid-ocean ridges, or rift vol- which should not contain stellar monopoles be- canic zones where tectonic plates slowly move cause they fail one of the search criteria, were away from each other, are also of interest. Lava also included: crust-derived lavas from a sub- flows from Gakkel Ridge (Arctic Ocean) [53, 54] duction zone (Antarctic Peninsula), and sam- provide attractive samples at very high lati- ples from a hotspot or mid-ocean ridge at low tude (84◦ N). Finally, some rock samples were latitude (Hawaii, Mid-Atlantic Ridge and East selected on the basis that chemical analysis Pacific Rise). The samples were shaped ei- reveals hints of deep mantle origins. Some ther as cylinders of 2.5 cm diameter and about basaltic lavas from Coleman Nunatak (Marie 2.5 cm length, or crushed into fragments, which Byrd Land, Antarctica) contain particularly were placed into plastic cuboid boxes 2.3 cm on high 206Pb/204Pb ratios (denoted as high µ, one side. The analysed samples are listed in Ta- or HIMU), which indicates low extent of melt- ble I and amount to a total of 23.4 kg of search ing and relatively deep origin [55]. In addition, samples and 1.2 kg of control samples. some of the lavas carry nodules of lherzolite,

Samples were measured with a 2G Enter- cluding measurements where the sample is in- prises, model 755R, 3-axis DC-SQUID rock side the sensing coils as well as 50 cm away from magnetometer housed in a shielded room at the sensing coils before and after the pass. Oc- the Laboratory of Natural Magnetism, ETH casional passes with an empty sample holder Zurich. For magnetic dipoles the current re- were made for background subtraction. The verts to zero on complete passage through the persistent current is deﬁned as the measured magnetometer superconducting coils. However, value after pass minus the value before pass a monopole would leave the signature of a per- (subtracting the same quantity for the empty sistent current. This technique allows us to di- holder), normalised such as to give the strength rectly measure the magnetic charge contained of magnetic pole contained in the sample in inside a sample without the need to extract units of gD. As described in detail in [59], cal- monopoles and with no mass dependence. Cur- ibration was performed using the convolution rent measurements were performed in steps, in- method, which consists of proﬁling the magne- 4

tometer response as a function of distance for a sample with well-known magnetisation and in- ferring the response for a monopole. As a calibration cross-check, the response to a magnetic pole was tested by introducing one extremity of a thin solenoid of 25 cm length with applied currents corresponding to values of magnetic charge of 0.124 gD, 1.24 gD, 12.4 gD and 124 gD. The two methods yield consistent results within a normalisation uncertainty of 10%.

Samples with a total magnetisation 1.5 ) 2 5 ≥ · 1.5D 10 gD (or magnetic dipole moment 4.4 5 2 ≥ · 1 10− Am ) were found to sometimes cause the flux-locked loop of the SQUID to be lost and 0.5 0 recovered at a different quantum level. This -0.5 leaves a signal similar to what is expected from -1 a monopole. Weaker moments generally did -1.5 not show this effect. Precautions were there- -2 1 2 3 4 5

fore taken so that all samples would have mag- persistent current (g 5 candidate number netisation levels below 1.5 10 gD. Crushing the sample material into a gravel-· or sand-sized powder randomises the magnetic moments from FIG. 1. Top: persistent current after first passage the constituent ferromagnetic minerals, which through the magnetometer for all samples. Bot- reduces the dipole signal. This method was fre- tom: results of repeated measurements of candidate quently used in this study. Alternatively, the samples with absolute measured values in excess of magnetisation can be reduced by more than an 0.25 gD. order of magnitude by exposing the sample to an alternating field. There is no risk of dislodg- ing a trapped monopole if a binding energy of current by an absolute value which deviates 100 keV or more is assumed. Demagnetisation from gD by less than 0.25 gD is about 0.3% was carried out only on 10% of the Antarctic (out of 678 samples, only the first candidate dis- samples probed in this study. cussed above satisfies this condition, but some Measurements of persistent currents after of the other candidates are close enough that we first passage through the magnetometer are conservatively assume two). The probability to shown for all samples in Fig. 1 (top). In the mismeasure the current in the direction where range from 0.1 to 0.1 g , the distribution is it would cancel out the current induced by a hy- − D Gaussian with mean value 0.002 0.001 gD pothetical monopole (whose charge can be pos- and standard deviation 0.026− 0.001±g . Non- itive or negative) is 1/2. Thus we obtain that ± D Gaussian tails slightly extend the distribution 0.3%/2=0.15% of the signals with g = gD | | beyond this range. Five candidates out of would escape detection; less if g > gD. It | | 678 samples yield absolute values which devi- is concluded that no monopoles with magnetic ate from zero by more than 0.25 g . The two charge g gD were present in the samples. D | |≥ first of these candidates yield the largest val- The most extensive meteorite search to date ues (0.8 gD and 1.6 gD) and also have total – the only other direct search with a non- 5 magnetisations in excess of 10 gD, close to the negligible sensitivity to stellar monopoles – sets 5 1.5 10 gD limit beyond which measurements a limit on the monopole density in meteoritic · 5 are known to be unreliable. Additional mea- material of less than 2.1 10− /gram at 90% surements of the five candidates using various confidence level. The study· analysed 112 kg orientations of the samples are shown in Fig. 1 of meteorites [35], among which 100 kg are (bottom). These multiple measurements con- chondrites and can thus be assumed∼ to consist firm the zero magnetic charge hypothesis. It is of undifferentiated material from the primary possible to get a rough estimate of the proba- solar nebula. This represents a little more than bility that a random sample containing a gen- 4 times more material than used in the present uine monopole with g = gD would yield a per- search. As discussed above, for monopole mass sistent current close| enough| to zero to remain and charge satisfying Equation 1 for a posi- unnoticed. The probability to mismeasure the tion above the core-mantle boundary, this dif- 5

ference can be compensated for by an increase [5] K. Kinoshita, R. Du, G. Giacomelli, L. Pa- in monopole concentration of roughly a factor 6 trizii, F. Predieri, et al., Phys. Rev. D 46, in polar mantle-derived rocks due to monopole R881 (1992) accumulation along the Earth’s magnetic axis. [6] J. L. Pinfold, R. Du, K. Kinoshita, B. Lorazo, M. Regimbald, et al., Phys. Lett. B 316, 407 One can think of two ways in which these re- (1993) sults on stellar monopoles could be further im- [7] G. R. Kalbfleisch, W. Luo, K. A. Milton, E. H. proved in the future: by probing large (> 100 Smith, and M. G. Strauss, Phys. Rev. D 69, kg) amounts of meteorites and polar rocks with 052002 (2004), arXiv:0306045 [hep-ex] a high-efficiency magnetometer, or by gaining [8] H1 Collaboration, Eur. Phys. J. C 41, 133 access to new types of samples such as asteroid (2005), arXiv:0501039 [hep-ex] and comet fragments. [9] CDF Collaboration, Phys. Rev. Lett. 96, 201801 (2006), arXiv:0509015 [hep-ex] In summary, massive monopoles of stellar ori- [10] OPAL Collaboration, Phys. Lett. B 663, 37 gins would be absent from planetary surfaces (2008), arXiv:0707.0404 [hep-ex] and would tend to accumulate along the mag- [11] ATLAS Collaboration, Phys. Rev. Lett. 109, netic axis in planets with internal magnetic 261803 (2012), arXiv:1207.6411 [hep-ex] fields. If monopoles in the mass range 103 [12] A. De Roeck, A. Katre, P. Mermod, D. Mil- m 1013 GeV are present within the Earth, stead, and T. Sloan, Eur. Phys. J. C 72, 1985 > (2012), arXiv:1112.2999 [hep-ph] they> would be expected to be found inside the [13] J. Preskill, Ann. Rev. Nucl. Part. Sci. 34, 461 Earth’s mantle below the geomagnetic poles. (1984) Assuming that monopoles bind strongly to nu- [14] D. H. Lyth and A. Riotto, Phys. Rep. 314, 1 clei, they would be trapped in mantle-derived (1999) rocks. This paper presents the first search for [15] J. Incandela, M. Campbell, H. Frisch, S. So- monopoles in polar igneous rocks. The search malwar, M. Kuchnir, and H. R. Gustafson, probed 23.4 kg of samples, for which a limit Phys. Rev. Lett. 53, 2067 (1984) 5 [16] M. W. Cromar, A. F. Clark, and F. R. Fickett, on the monopole density of 9.8 10− /gram at · Phys. Rev. Lett. 56, 2561 (1986) 90% confidence level is set, which in a simple [17] J. Incandela, H. Frisch, S. Somalwar, M. Kuch- 5 model translates into a limit of 1.6 10− /gram nir, and H. R. Gustafson, Phys. Rev. D 34, · in the matter averaged over the whole Earth. 2637 (1986) This search has a comparable or better sensi- [18] S. Bermon, C. C. Chi, C. C. Tsuei, J. R. tivity than the most extensive meteorite search Rozen, P. Chaudhari, M. W. McElfresh, and and provides a novel probe of stellar monopoles A. Prodell, Phys. Rev. Lett. 64, 839 (1990) [19] R. D. Gardner, B. Cabrera, M. E. Huber, and in the Solar System. M. A. Taber, Phys. Rev. D 44, 622 (1991) We are indebted to W. E. LeMasurier for pro- [20] M. E. Huber, B. Cabrera, M. A. Taber, and viding rock samples from Coleman Nunatak, to R. D. Gardner, Phys. Rev. D 44, 636 (1991) R. G. Trønnes for providing a sample from the [21] S. Orito, H. Ichinose, S. Nakamura, K. Kuwa- Beerenberg volcano, and to A. Kontny for pro- hara, T. Doke, K. Ogura, H. Tawara, M. Imori, viding us samples from Hawaii and H. B. Matts- K. Yamamoto, H. Yamakawa, T. Suzuki, K. Anraku, M. Nozaki, M. Sasaki, and son for additional samples from Iceland. This T. Yoshida, Phys. Rev. Lett. 66, 1951 (1991) research extensively used samples loaned from [22] MACRO Collaboration, Eur. Phys. J. C 25, the United States Polar Rock Repository, which 511 (2002), arXiv:0207020 [hep-ex] is sponsored by the United States National [23] SLIM Collaboration, Eur. Phys. J. C 55, 57 Science Foundation, Office of Polar Programs. (2008), arXiv:0801.4913 [hep-ex] This work was supported by a fellowship from [24] BAIKAL Collaboration, Astropart. Phys. 29, the Swiss National Science Foundation and a 366 (2008) [25] D. P. Hogan, D. Z. Besson, J. P. Ralston, grant from the Ernst and Lucie Schmidheiny I. Kravchenko, and D. Seckel, Phys. Rev. D Foundation. 78, 075031 (2008), arXiv:0806.2129 [astro-ph] [26] IceCube Collaboration, Eur. Phys. J. C 69, 361 (2010) [27] ANITA-II Collaboration, Phys. Rev. D 83, 023513 (2011), arXiv:1008.1282 [astro-ph] ∗ [email protected] [28] ANTARES Collaboration, Astropart. Phys. [1] P. A. M. Dirac, Proc. Roy. Soc. A 133, 60 35, 634 (2012), arXiv:1110.2656 [astro-ph] (1931) [29] J. Beringer et al. (Particle Data [2] P. A. M. Dirac, Phys. Rev. 74, 817 (1948) Group), Phys. Rev. D 86, 010001 (2012), [3] G. ’t Hooft, Nucl. Phys. B 79, 276 (1974) http://pdg.lbl.gov [4] K. A. Milton, Rep. Prog. Phys. 69, 1637 [30] E. Goto, H. H. Kolm, and K. W. Ford, (2006) Phys. Rev. 132, 387 (1963) 6

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